Section 5: Debt
Concepts you’ll learn
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6.
7.
Nominal interest rates
Compounding
Credit scores and consequences
The time value of money
Secured loans and common terms
Amortization
Revolving credit and common terms
Problems you’ll solve
– Calculate nominal interest earned – compounded annually vs.
monthly
– Calculate the cost of paying higher interest rates
– Deconstruct loan terms and proposals
– Deconstruct amortization schedules
– Deconstruct credit card offers
©2014 D. M. Kaufman. All rights reserved
Debt – Definitions
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Debt: An obligation or liability to pay or render something to another entity – a.k.a. a loan. In personal finance, most debts
are in the form of money received today in exchange for a promise of re-payment of the original amount, or principal, plus
interest.
Principal: The original amount of a debt or loan.
Interest Rate: A sum paid for the use of money or for borrowing money. Usually expressed as a percentage. The interest
rate associated with a given loan will typically be related to prevailing interest rates in the macro-level economy at the time
the loan is originated.
Nominal Interest Rate: An interest stated as a flat annual percentage on the principal, with no provisions made for
compounding, inflation, etc.
Annual Percentage Rate (APR): The interest that has to be paid on a loan, plus all other costs – e.g. the cost of originating
the loan (banks don’t work for free), points, etc.
Annual Percentage Yield (APY): Also known as the effective annual interest rate. This number is primarily affected by the
frequency of interest compounding.
Simple Interest: Interest paid on the principal only.
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Compound Interest: Interest which is calculated not only on the initial principal but also the accumulated interest of prior
time periods.
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e.g. I borrow $1,000 for two years at 10% annual interest, to be compounded annually. At the end of the first year I still owe the original $1,000,
plus the first year’s 10% interest of $100 gets added to the tally, so I now owe $1,100. At the end of the second year, I need to repay the $1,000
principal, plus the $100 interest from the first year, plus the second year’s interest on the principal (another $100), plus 10% interest on the $100
that accrued as interest during the first year, or another $10. So my total repayment will be 1000+100+100+10 = $1,210.
Amortization: The gradual elimination of a loan in regular payments over a specified time period. The idea is to provide the
borrower with a fixed periodic payment over the life of the loan – say, $500 each month – as opposed to nailing the borrower
with a huge “balloon payment” at the end of the loan as in our “compound interest” example above.
Secured Debt: Loan amount for which the borrower pledges one or more assets of equal or greater liquidation value as a
security (also called collateral) which may be forfeited in case of a default (failure to pay). Also called secured loan.
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e.g. I borrow $1,000 for one year at 10% interest. At the end of the year I pay back the original principal of $1,000 plus interest of (1000*.10) =
$100 for a total repayment of $1,100. The $100 is simple interest.
e.g. Houses and cars. Fail to make your payments, and whomever loaned you the money to buy your house or car will repossess it from you.
Unsecured Debt: A debt offering or loan that is backed only by the reputation and credit-worthiness of the borrower, with
no collateral offered as security.
Revolving Credit: A line of credit (e.g. a credit card) in which any available credit underneath a maximum credit limit is
available for withdrawal at any time. Interest is charged only on the outstanding balance at the end of a given time period,
and full repayment can be made at any time without penalty.
Pre-Payment Penalty: Additional fee imposed by some loan agreements where a borrower repays a loan before its
scheduled pay-off date.
Mortgage: Technically, another name for a secured loan. But in common parlance, it refers to a loan taken out for the
purpose of buying real estate, with the real estate itself serving as collateral.
Points: Finance charges paid by the borrower at the beginning of a loan. One point is 1% of the loan amount.
Some Geeky Interest Formulae
• Just to give you a hint of how God-awful this stuff used to be
before the advent of financial calculators...
– Simple interest can be expressed by the formula I = P*r*t, where I is the interest
amount you’re solving for; P is the principal; r is the interest rate; and t is the lifetime of
the loan in years.
• e.g. You borrow $5,000 at 8% for five years. The simple interest will be: 5000*.08*5 = $2,000.
– Compound interest is a bit more complex. When you’re paying interest on the interest
the formula becomes M = P(1+i)n, where M is the total amount to be paid back,
including principal; P is the principal; i is the interest rate; and n is the number of times
the interest is compounded during the entire life of the loan.
• e.g. You borrow $5,000 at 8% for five years, with the interest compounded annually. M =
5000(1+.08)5 = 5000(1.08)5 = 5000(1.47) = $7,346.64. Since the principal was $5,000, the
total compounded interest is 7346.64 – 5000 = $2,346.64.
• Notice that the effect of compounding is to increase the total amount of interest paid. That’s a
very powerful concept, and it’s vital in financial planning, investing, retirement planning, etc.
• Also notice that this formula can very quickly become unwieldy to perform by hand. Imagine that
the interest over the five years is to be compounded monthly instead of annually. Anyone want
to do M = 5000(1+.08)60 by hand? Didn’t think so. We’ll be using our calculator’s financial
functions for this sort of thing.
– Amortization is so complex that I’m not even going to give you a non-calculator
example. But, just so you have it, the formula is:
The only new symbol is A, which represents the regular periodic payment, but still, this
is a bear. We’ll use the calculator.
Now, a Super Special Definition
• Time Value of Money (TVM): The idea that a dollar now
is worth more than a dollar in the future, because a
dollar now can earn interest or other appreciation until
the time the dollar in the future would be received.
– This is the reason interest is charged on loans. A lender needs to be
rewarded for giving up the use of money for the time period of the loan. If
the lender simply receives back the principal at the end of the life of the
loan, the lack of interest or any other return represents an opportunity cost
(remember that one?) that can never be recovered.
– There are many, many scenarios surrounding TVM calculations, and not all
of them have to do with loans, but all of them are based on the following
variables:
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The
The
The
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principal amount, also known as the present value, or PV
interest rate
number of time periods (years, months, etc.)
regular periodic payment, if any
future value of the money flow, or FV
– You can solve for any one of the above variables if you know the other four
– Your financial calculator has functions specifically designed to solve TVM
problems for you. For each type of problem, I’ll give you the geeky
formula just as trivia, and then show you how to truly solve for it with your
calculator.
Your Calculator’s TVM Functions
Regular Functions
Shift Functions
xP/YR: Number of periods per year
NOM%: Nominal Interest Rate
EFF%: Effective Interest Rate
P/YR: Payments per year
AMORT: Amortize
“Shift” Key: Press this first to activate any of
the orange calculations on the function keys
“Clear” and “Clear All” – you’ll need to hit Shift then
Clear All to dump your calculator’s memory in many
instances. I do it all the time just out of habit.
Learn how to use these function keys well, and no one will ever be
able to mislead you regarding personal loans, mortgages, etc. You’ll
use these same keys for investment scenario and retirement
planning as well. TVM is powerful stuff.
TVM Example #1: Compound Interest
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Here’s the formula again: M = P(1+i)n
Let’s start with something simple. Essentially we’ll be solving for M.
First, set up your calculator for annual periods
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Now, let’s re-do our example from a few pages ago, using the calculator functions:
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Press 1, then press shift, then press P/YR
All your TVM functions will now assume that interest compounds on an annual basis (1 period per year, or 1P/YR)
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You borrow $5,000 for 5 years at 8% compounded annually.
The present value of your loan is the $5,000 you’re receiving today, so key in 5000, then press PV
Your interest rate is 8%, so hit 8, then press I/YR (the calculator will do the percentage conversion for you)
The life of your loan is five years, so hit 5, then shift, then xP/YR
You’re not making any regular periodic payments in this example, so hit 0, then PMT
Now, hit FV. You should get -$7,346.64 This is the total amount you’ll pay.
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Now add back in the original principal you received at the beginning of the loan to isolate the total interest that
you’ll have to pay:
-7346.64 + 5000 = -$2,346.64
If you feel better flipping the negative sign to a positive, do it at the end by hitting the +/- button. Some people
are better able to keep things straight in their own heads that way.
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Note the negative number! That’s because this is money you’ll have to pay out at the end of the loan. Money flowing to
you is positive, and money flowing from you is negative. Always.
Now, let’s do the same problem, but with interest compounded monthly:
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Set up your calculator for monthly periods. Key in 12, then press shift, then press P/YR. All your TVM functions will
now assume that interest compounds on a monthly basis (12 periods per year, or 12P/YR)
Key in 5000, then press PV. Hit 8, then I/YR. Hit 5, then shift, then xP/YR. Hit 0, then PMT. Hit FV.
You should get -$7,449.23. To isolate the interest, add back in the $5,000 to get -$2,449.23.
Again, notice that more frequent compounding  more interest paid.
Here’s the cool part. If you want to run through scenarios, you can change just one
variable, then hit FV again to get your new answer.
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i.e. Hit 10, then hit I/YR to boost the annual interest rate to 10%. Hit FV. You should now get -$8,226.54.
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i.e. Someone convinces you to pay $10,000 in five years to receive $6,000 today. Want to know what interest
rate you’d be agreeing to?
Hit 6,000, then PV
Hit -10,000 (note the negative – you’ll be paying this money out), then FV
Hit 5, then shift, then xP/YR
Hit 0, then PMT
Hit I/YR.
You’d be agreeing to pay 10.26% annual interest, compounded monthly.
More cool stuff: you can solve for things other than just the FV.
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By the way, in life, most loans and interest compound monthly, so it’s a good idea to
leave your calculator set up for 12P/YR unless a certain rare situation (like an exam
question, maybe) requires otherwise.
TVM Example #2: Nominal Interest vs. APY
• Remember, the Annual Percentage Yield (APY) is the
effective interest rate after considering the effects of
compounding more frequently than once per year
• Here’s the formula: APY = (1 + r/n )n – 1
– r is the stated (or nominal) interest rate
– n is the number of times per year the interest will be compounded
• Here’s how you do it on your calculator
– First, just to set the stage, program your calculator to compound interest
on an annual basis only
• Press 1, then shift, then P/YR
• Clear all
– Now, give your calculator a nominal rate of 10%
• Key in 10, then press shift, then NOM%
– Solve for the effective rate by pressing shift, then EFF%
• The calculator should spit 10% back at you, since you’ve got it set up to
compound the interest only once per year
• Clear all
– Now, re-program your calculator to compound interest monthly
• Key in 12, then press shift, then P/YR
– Key in a nominal interest rate of 10% again, then press EFF%
• The number changed, right? You should now get 10.47%
• This is huge. Most loan advertisements will state the nominal rate, yet the
interest on most loans is compounded monthly, which brings the APY or effective
rate up. Remember that.
TVM Example #3: Amortized Loans
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Now we add regular periodic payments into the mix
Here’s the formula again:
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Let’s keep your calculators programmed for 12 periods per year
Here’s the scenario:
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You borrow $10,000 to pay for a car, and the bank offers you an 8% interest rate for five years.
What will your monthly payment be?
Key Point: In this example, you’re paying the loan off over the five years with regular monthly
installments, and at the end of the five years the loan will be fully repaid. Since you owe nothing at
the end of the loan, the future value is... zero.
So, input a present value of 10,000
Input an interest rate of 8%
Input the number of periods by pressing 5, then shift, then xP/YR
Input a FV of 0
Press PMT
You should get an answer of -$202.76 (this equates to the variable A in the formula)
Now, what would your payment be if the interest rate were 10%?
How about 6%?
This is precisely how most secured loans (for cars, for homes, etc.) work.
Now, let’s say you’re seated across from a car salesperson. He offers you
the following terms to buy a car with a sticker price of $15,000:
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Down payment of $3,000
Monthly payment of $350 for five years
Assuming that you’re actually paying $15,000 for the car, what interest rate would you be agreeing
to?
In this example, you’re solving for the interest rate. You know that the present value of the loan is
15,000 - 3,000 = 12,000. You know that the FV is 0. You know that the PMT is -$350 (note the
negative number!). And you know that the life of the loan is 12P/YR*5 = 60. Ask the calculator for
the I/YR.
You should get 24.68% That’s pretty high.
Congrats – you’ve just solved for the variable r in the formula
TVM Example #3: Amortized Loans (continued)
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Let’s change the scenario a bit
Same car, same sticker price of $15,000
The salesperson still offers you the car for a down payment of $3,000, plus
payments of $350/mo for five years, but...
...you’ve been pre-approved by your bank to borrow up to $20,000 to buy a
car at 10% interest.
The damn sales person sticks to his guns on the terms, and evades all your
attempts to get him to divulge the effective price you’d be paying for the
car. So you need to calculate it yourself to negotiate effectively. You need
to solve for PV (or the variable P in the amortization formula).
So, input the following:
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5  shift  xP/YR
10  I/YR
-350  PMT
0  FV
Press PV. You should get $16,472.88
Now, wait! All you’ve done so far is calculate the present value of your payment stream of $350/mo
for five years at 10% interest. The terms also demand a down payment from you of $3,000. You
need to add that back in to identify the total PV of the terms offered. So 16,472.88 + 3,000 =
$19,472.88.
In other words, you’d be agreeing to pay almost $20,000 for a $15,000 car even though the
dealership often expects people to pay something lower than the sticker price. This is a bad offer.
But if you confront the sales person with this info, you’ll finally be able to negotiate on the basis of
the price itself, which is something many car dealers desperately try to avoid.
By the way, this is the exact same sequence you’d go through if you want
to identify how expensive a car you can afford to buy. If you know 1) what
you can afford to pay up front, 2) what you can afford to pay each month,
3) what interest rate you’re approved for, and 4) the lifetime of the loan,
then you can solve for PV, add in you down payment, and... voila. That’s
the price you can afford to pay.
TVM Example #3: Amortized Loans (continued)
• One last concept on amortization:
– With an amortized loan, your early payments will mostly be applied to interest,
since the principal is still so high in the early stages. Over time, less of each
payment will get applied to interest and more will get applied to principal.
• So, if you decide to pay off an amortized loan early (either
by paying it off free and clear or by re-financing and
getting into a new loan), how do you know, at any point in
time, how much principal you still owe?
• See how on the next page...
TVM Example #3: Amortized Loans (continued)
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Make sure your calculator is programmed for 12P/YR
Now, let’s say you’ve taken out the following mortgage to buy a home:
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The first step is to input all known variables into your calculator, so...
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Now, let’s say you’re ten years into the loan, and you want to know 1) how much of
your most recent payment went towards principal, 2) how much of it went towards
interest, and 3) how much principal is left to be paid off. Follow these steps:
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$500,000 @ 6.5% fixed rate over 30 years
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Input
Input
Input
Input
Press
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Press 120 (after ten years, you’ll have made 120 monthly payments), then press INPUT (right below the N key)
Now, press shift, then AMORT (upper right corner, in orange letters)
The calculator will confirm for you the payment range being broken down for you (in this case, the 120 th payment
through the 120th payment)
Press the “=“ button once, and the calculator will show you the amount of the 120 th payment applied to principal
Press “=“ again, and you’ll get the amount of the 120 th payment applied to interest
Press “=“ again, and you’ll get the principal (or balance) still owed after you’ve made the 120 th payment
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the PV of 500,000
the I/YR of 6.5
the time periods of 30  shift  xP/YR
the FV of 0 (since the loan will be paid off at the end)
PMT to calculate for the monthly payment. You now have all five variables identified.
Here’s the scary part. Notice that after ten years (1/3 of the lifetime of this loan), you
still owe 85% of the original amount you borrowed. Whoa.
Just to get really freaked out, now amortize the 240th payment. #*@%! Now you’ve
made 2/3 of the total payments on this loan, and you still owe more than half of the
principal.
Here’s the good news: if you pay more than the required amount each month, and you
give your lender instructions to do so, they will apply the extra money directly to the
principal, and you’ll get your loan paid off way early. Want to find out approximately
how early? Here’s how:
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Input all the known variables as described above
After you’ve solved for the payment, you’ll decide how much you can really afford each month. In this case let’s say
it’s $4,355.54. So input -4.355.54 (remember the negative – you’re paying this money out), then press PMT.
Now, press N.
You should get 180 monthly payments total. That equates to 15 years. So by paying an extra not-quite $1,200/mo,
you’ve cut the lifetime of the loan in half.
Conversely, you could input your desired loan lifetime and then solve for the new required PMT.
A Bit More on Mortgages
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Your home is likely to be the most expensive item you’ll buy in
this life, so here are a few extra facts about the associated loans
you’ll have to evaluate:
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You can typically finance (borrow) 80% of the value of a home with a single, or primary,
mortgage without having to pay “mortgage insurance.” This means you take out an
insurance policy guaranteeing payment to your mortgage lender if you default, and... you
get to pay the premiums.
A potentially better way to go if you want to finance more than 80% is to take out a second
mortgage, but the interest rate on that second mortgage will be higher than on the primary
mortgage, so...
...The best way to buy a home is to come up with 20% down, but that can be tough for a
first time home buyer in this day and age.
Mortgage lenders will evaluate your ability to pay based on a little something called PITI,
which stands for Principal, Interest, Taxes, and Insurance. That is, they’ll assess whether
you’ll likely be able to repay the principal and interest, of course, but they also want to be
sure you can pay the property taxes and pay to insure the home – until your loan is paid
off, the lender counts on the home as collateral (or security) in case you default, so they
require it to be insured. But – ha ha! – they’re not going to pay the premiums; that’s your
responsibility.
You will be confronted with the option to take out a fixed rate loan or a variable rate loan.
They both have pros and cons. Here’s the breakdown:
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Fixed Interest mortgages are, as the name suggests, mortgages for which the interest rate does not
change during the lifetime of the loan, which is typically either 15 or 30 years. 15 year mortgages will
typically carry lower interest rates than 30 years, but the payments will (obviously) be higher since
the loan is paid off in half the time. Fixed rate mortgages allow your to budget a fixed amount on
housing until you either pay off the entire loan, or move to a new house. And, as time passes, your
income is likely to rise, and inflation will devalue the fixed number of dollars you use for your monthly
payments – i.e. in inflation adjusted terms, your monthly payment will decrease.
Variable Interest or Adjustable Rate Mortgages (ARMs) are mortgages for which the interest rate
fluctuates per a regular, pre-agreed schedule. The interest rate will typically be lower than that of a
fixed rate mortgage at any given time, but if prevailing interest rates go up the scheduled rate re-set
can trigger a higher monthly payment than the fixed rate offered at the loan’s origination. If the
resultant payment proves unaffordable, the borrower’s choices quickly get reduced to 1) sell the home
and move somewhere else, 2) attempt to refinance for a lower monthly payment, which unfortunately
re-starts the clock on paying off the debt, or 3) default. ARMs can be great for people who know that
they’ll live in a house for only a short time (since they’ll pay a lower interest rate for that short time)
and are confident they’ll be able to sell the home in a timely fashion. But... they can be very
dangerous.
A Bit on Credit Cards
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Credit Cards are a perfect example of “revolving credit” – you borrow
what you like (subject to credit limits) and pay the principal back
whenever you like (although minimum interest payments will be due
monthly).
They can be very convenient, and can provide excellent fraud security
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But... there are a few pitfalls to be wary of.
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i.e. If your card is lost or stolen, and you notify your credit card company as soon as you realize it,
the most you’ll be obligated to pay for any fraudulent charges, under federal law, is $50 (per card).
Introductory interest rates: Credit card companies will often try to tempt you by offering below
market rates for initial purchases or balance transfers, but this rate expires after a certain amount
of time, which is usually disclosed in the offer in very fine print. If you carry any balance beyond
that expiration date, the interest on that balance will immediately shoot up – sometimes to above
market rates. A lot of people get burned this way.
Late Fees: Take special note of the due date for your monthly payments. Miss it, and the credit
card company will tack on a fee, and they may use it as an excuse to increase your interest rate.
Credit Limits: Make sure you don’t attempt to borrow more than your limit at any given time. If
you do, you may get hit with a penalty and with a higher interest rate moving forward.
Minimum Payments: It can be tempting to run out buy $10,000 worth of frivolous crap with a new
credit card, knowing that you’ll only have to pay a small fraction back each month until you feel
good and ready to pay back the whole thing. But interest rates on credit cards can exceed 20%,
and the minimum payment is typically small enough to keep you in debt for a very, very, long time
if you let it. A good rule of thumb credit card companies use is: if you make only the minimum
payment to pay off a given balance, you’ll stay in debt long enough to fork over the principal, plus
~2x the principal in interest. Some companies are even more predatory and will set the minimum
payment so that your principal debt actually grows over time and, if it ever exceeds your credit
limit, they’ll hit you with penalties, fees, and ratchet up your interest rate. When you wake up to
find out what has happened to you, they’ll point to the very fine print in the credit agreement you
signed.
The most advantageous way to use your credit card is to use it to buy
only what you can afford to buy with cash, and pay off your balance
every month to avoid all late fees and all interest charges
And Now, a Word From Our Sponsor: FICO
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Fair Isaac Credit Organization = FICO, which is expressed as a creditworthiness score ranging from
~300 to ~900 (higher is better)
Your FICO score will greatly determine the interest rates offered to you for various forms of credit
and/or debt.
Your FICO score is derived from all kinds of credit history data on you, all of which is reported to and
shared by three major credit reporting organizations (in the U.S.): Experian, TransUnion, and Equifax.
All lenders have access to your credit report and will check it before extending any credit to you.
What sort of credit history data? e.g....
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Payment History
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Account payment information on specific types of accounts (credit cards, retail accounts, installment loans, finance company accounts,
mortgage, etc.)
Presence of adverse public records (bankruptcy, judgments, suits, liens, wage attachments, etc.), collection items, and/or delinquency (past
due items)
Severity of delinquency (how long past due)
Amount past due on delinquent accounts or collection items
Time elapsed since any past due items (delinquency), adverse public records (if any), or collection items (if any)
Number of past due items on file
Number of accounts paid as agreed
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Amount owing on accounts
Amount owing on specific types of accounts
Lack of a specific type of balance, in some cases
Number of accounts with balances
Proportion of credit lines used (proportion of balances to total credit limits on certain types of revolving accounts)
Proportion of installment loan amounts still owing (proportion of balance to original loan amount on certain types of installment loans)
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Time since accounts opened
Time since accounts opened, by specific type of account
Time since account activity
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Number of recently opened accounts, and proportion of accounts that are recently opened, by type of account
Number of recent credit inquiries
Time since recent account opening(s), by type of account
Time since credit inquiry(s)
Re-establishment of positive credit history following past payment problems
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Number of (presence, prevalence, and recent information on) various types of accounts (credit cards, retail accounts, installment loans,
mortgage, consumer finance accounts, etc.)
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Amounts Owed
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Length of Credit History
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New Credit
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Types of Credit Used
• The more stable and able to pay you appear, the higher your FICO score and the more favorable your
borrowing terms will be.
• You have the right under federal law to check your own credit rating once each year, free of charge.
Go to www.myfico.com for more details.
• If your FICO score is too low for favorable terms, consider finding a co-signer with better credit. Your
co-signer will also be responsible for the loan, but the offered interest rate should decrease.
Section 5: Practice Problems
1.
True or false?
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The nominal interest rate and the effective interest rate are pretty much the same.
Interest compounding has a dramatic impact on interest paid over the life of most loans.
The value of a dollar today is higher than that of a dollar tomorrow.
Your loan payment record with one bank will not be considered if you apply to another bank for a loan.
If one of your credit cards gets lost or stolen, and you report it as soon as you realize it’s gone, you could still be liable
for all fraudulent charges.
Define Present Value (PV).
Define Simple Interest.
Define Compound Interest.
What’s PITI?
If you borrow $1,000 for 5 years at 8%, how much will you owe at the end
of the loan if the interest compounds annually?
7. (building on the previous question) How about if it compounds monthly?
8. Say you want to buy a car and the MSRP is $25,000. You have a $5,000
down payment but no trade-in. The nice salesperson offers you the car for
your $5,000 plus $500/mo for five years. What effective interest rate
does this deal charge you?
9. Assume you take the deal offered in the previous question, but assume you
brought in pre-approved financing for 8%. You make all your payments
and own the car free and clear after the five years. What effective price
did you really pay for the car?
10. Fifteen years ago you borrowed $400,000 to buy a home with a 30-year
fixed rate mortgage with an interest rate of 6.75%. So, you just made
your 180th payment.
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How much of that 180th payment went toward paying down the principal?
How much of it went towards paying interest?
How much of the loan principal remains to be paid (in other words, what’s the remaining balance)?