College Costs, Loans, and Credit Cards




Frequently, college costs are given on a per
semester basis. It is important to double this
value to account for a full year of college costs.
On top of the tuition and fees, books, and other
random costs associated with school, you also
need to factor in a variety of monthly costs.
These monthly costs could just be spending
money (if you live in the dorm and don’t have a
car or cell phone), or could be as extensive as
rent, food, insurance, gas and repairs, cell phone,
and spending money.
All of these costs must be considered when
considering attending college.

For any loan, the principal is the amount of
money owed at any particular time. Interest is
charged on the loan principal. To pay off a
loan, you must gradually pay down the
principal. Therefore, in general, every
payment should include all the interest you
owe plus some amount that goes toward
paying off the principal.


About two-thirds of all college students take
out student loans, with an average debt of
about $20,000 at graduation.
There are two main types of student loans.


A subsidized student loan is a loan that does
not require you to pay interest while you are
enrolled in school. During that time, the
federal government pays the interest. But
after you graduate and your grace period
(usually 6 months) ends, you must start
paying back your loans and interest.
Subsidized loans are based on financial need.
The subsidized Stafford Loan and the Perkins
Loan are classified as subsidized loans.


An unsubsidized student loan is a loan that
requires you to pay back the interest on the
loan while you are in school. Like a
subsidized student loan, payment on your
principal is deferred until six months after
graduation, but instead of the school or
government picking up the tab on interest, it
is all up to you.
Reference: ehow.com



Subsidized loans have a tight cap on how much
you can borrow per year and are dependent upon
your specific situation and financial status.
An unsubsidized loan also has a cap on it, but it
is much higher than the subsidized loan.
Basically, you can borrow between $4,000 and
$5,000 more per year during your undergraduate
career.
When you have reached the cap on borrowing
money through a subsidized loan, the only other
option is an unsubsidized loan. It is very possible
that you will end up with a combination of the
two.


A loan that you pay off with equal regular
payments is called an installment loan (or an
amortized loan).
This is the type of loan that is offered most in
our society and includes:
◦ Home loans
◦ Car loans
◦ Student loans
𝐴𝑃𝑅

𝑃∗( 𝑛 )
𝑃𝑀𝑇 =
[1−
𝐴𝑃𝑅 −𝑛𝑌
1+ 𝑛
]
◦ PMT is the amount of the payment
◦ P is the starting principal of the loan (amount
borrowed)
◦ APR is the annual percentage rate
◦ n is the number of compounding periods per year
◦ Y is the loan term in years
1.
2.
You have a total of $50,000 in student
loans with a fixed APR of 6% for 20 years.
How much are your monthly payments? How
much did you repay in total for this loan?
You borrow $12,500 over a period of 5
years at an APR of 12%. How much are your
monthly payments? How much did you
repay in total for this loan?
1. You have a total of $50,000 in student loans
with a fixed APR of 6% for 20 years. How much are
your monthly payments? How much did you repay
in total for this loan?
Solution: With P = 50,000, r = 6% = 0.06, Y = 20
and n = 12 (monthly) we can find the payments as
0.06
50,000( 12 )
𝑃𝑀𝑇 =
(1−
0.06 − 12𝑥20
1+ 12
= $358.22. Our payments will
)
be $358.22. We pay this amount every month for
20 years to get 358.22 x 12 x 20 = $85,972.80
repaid in total.
2. You borrow $12,500 over a period of 5
years at an APR of 12%. How much are your
monthly payments? How much did you repay in
total for this loan?
Solution: Substituting values into the formula
0.12
)
12
0.12 − 12𝑥5
1+ 12
12,500(
we find 𝑃𝑀𝑇 =
(1−
= $278.06. We
)
pay this amount every month for 5 years to get
278.06 x 12 x 5 = $16,683.60 repaid in total.
3.
4.
You borrow $150,000 over a period of 30
years at a fixed APR of 4%. How much are
your monthly payments? How much will
you repay in total for this loan?
Your student loan total is $24,000 with a
fixed APR of 8% for 15 years. How much
are your monthly payments? How much
will you repay in total for this loan?
3. You borrow $150,000 over a period of 30
years at a fixed APR of 4%. How much are your
monthly payments? How much will you repay in
total for this loan?
Solution: Using the formula you should find
PMT = $716.12. Paying this amount every
month for 30 years, a total of 360 payments,
you pay $257,803.20 for your loan.
4. Your student loan total is $24,000 with a
fixed APR of 8% for 15 years. How much are
your monthly payments? How much will you
repay in total for this loan?
Solution: Using the formula you should find
PMT = $229.36. You will repay a total of
$41,284.80 for this loan.


The portions of installment loan payments
going toward principal and toward interest
vary as the loan is paid down. Early in the
loan term, the portion going toward interest
is relatively high and the portion going
toward principal is relatively low. As the term
proceeds, the portion going toward interest
gradually decreases and the portion going
toward principal gradually increases.
We will discuss this more in detail when we
discuss home mortgages.



Credit cards are different from installment loans
in that you are not required to pay off your
balance in any set period of time.
Instead, you are generally required to make only
a minimum monthly payment that generally
covers all the interest but very little principal. As
a result, it takes a very long time to pay off your
credit cards if you make only the minimum
payment.
If you wish to pay off your credit cards in a
certain amount of time, you should use the loan
payment formula to calculate the necessary
payments.


There is a 56 minute video from PBS Frontline
talking about The Secret History of the Credit
Card.
If you would like to view it, please google the
terms above and it will be displayed.
1.
2.
You have a credit card balance of $2300 with
an annual interest rate of 21%. You decide to
pay off your balance over 1 year. How much will
you need to pay each month? Assume you make
no further credit card purchases.
Your New Year’s resolution is to stop using
your credit card and get it paid off. You have
$5000 on the card with an APR of 18% and you
want to pay off the balance in one year. How
much will you need to pay each month? How
much will you have repaid on this card?
1. You have a credit card balance of $2300 with
an annual interest rate of 21%. You decide to pay
off your balance over 1 year. How much will you
need to pay each month? Assume you make no
further credit card purchases.
Solution: Using the same formula as we did for
loans with P = 2300, r = 0.21, Y = 1 and n = 12
(monthly) we get PMT = $214.16. (Notice that we
cannot just divide 2300 by 12 to get the amount of
payment; that method does not take into account
the interest.)
2. Your New Year’s resolution is to stop using
your credit card and get it paid off. You have
$5000 on the card with an APR of 18% and you
want to pay off the balance in one year. How
much will you need to pay each month? How
much will you have repaid on this card?
Solution: You should get PMT = $458.40. You
will repay a total of 458.40 x 12 = $5500.80.
Only $500 more than the original amount due,
not too bad.


Your card has an APR of 20% and you want to pay
the balance of $21,656 off in 3 years. If you
stopped using the card immediately, how much
will you need to pay each month? How much will
you have repaid in total on the card?
Your card has an APR of 12.5% and you want to
pay the balance of $3000 off in 3 years. Assume
no further charges are made. How much will you
need to pay each month? If you paid it off in 1
year instead, how much would you need to pay
each month? Compare the totals repaid and
determine which is a better idea.



Your card has an APR of 20% and you want to pay
the balance of $21,656 off in 3 years. If you
stopped using the card immediately, how much
will you need to pay each month? How much will
you have repaid in total on the card?
Solution: For your credit card with $21,656 to be
paid in 3 years your payments would be PMT =
$804.81. You will repay a total of $28,973.16 on
this credit card.


Your card has an APR of 12.5% and you want to
pay the balance of $3000 off in 3 years. Assume
no further charges are made. How much will you
need to pay each month? If you paid it off in 1
year instead, how much would you need to pay
each month? Compare the totals repaid and
determine which is a better idea.
Solution: If you pay your balance in 3 years you
will have PMT = $100.36 with $3612.96 paid in
total. However, if you pay it off in 1 year you will
have PMT = $267.25 with $3207.00 paid in total.
You will save over $400 if you pay it in one year,
but the payments are significantly higher.




Credit cards can be a good thing when used
correctly. They can also turn in to a
nightmare when used poorly.
Use only one credit card.
If possible, pay off your balance in full each
month.
If you plan to pay off your balance each
month, make sure your card has an interestfree grace period.





Compare the interest rate and annual fee.
Watch out for teaser rates.
Never use your card for cash advance except
in case of an emergency.
If you own a home, consider replacing a
common credit card with a home equity
credit line. You’ll generally get a lower
interest rate, and the interest may be tax
deductible.
Never fear consulting a financial advisor if
you get in a hole.

You can now complete problems 1.8 – 1.12 in
Jack Appreciates Math chapter one.