Computer Science & Engineering 4194
Day 9
Financial Functions
1
Financial Functions
• Functions that can be used to calculate values
based on compounded interest
– Taking a loan
– Investing in a savings account
2
Simple Interest vs. Compound Interest
• Simple interest always calculates interest based on the
original amount.
So $1,000 at 4% per year for 2 years
• Year 1: $1000 * 4%  $40 in interest for the 1st year.
• Year 2: $1000 * 4%  $40 in interest for the 2nd year.
After 2 years you would have:
$1,000 * 4% = $80 interest
For a total of $1,080
3
Simple Interest vs. Compound Interest
• Compound interest always calculates interest based on the
“latest amount”.
So $1,000 at 4% per year for 2 years compounded Yearly
• Year 1: $1,000 * 4%  $40 in interest for the 1st year.
• Year 2: $1,040 * 4%  $41.60 in interest for the 2nd year.
After 2 years you would have:
$1,000 * 4% = $81.60 interest
For a total of $1,081.60
Simple Vs. Compound Interest
$1,000 after 2 Years at 4%
$82.00
$81.50
$81.00
$80.50
$80.00
$79.50
$79.00
Simple Interest
Compound Interest
4
Compounding Periods
• Compounded Yearly
• Compounded Quarterly
– 4 quarters per year and 3 months per quarter
• Compounded Semi-Annually
– 6 months per half year
• Compounded Monthly
– 12 months per year
• You *cannot* assume 30 days per month
The total amount of your financial transaction will
be different based on when the interest is
compounded.
5
Compounding Interest Quarterly
What if we compound our 4% interest quarterly for the $1,000.
This would be four separate calculations
Quarter
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
Principal
$1,000 * 1%
$1,010 * 1%
$1,020.10 * 1%
$1,030.301 * 1%
Interest
= $10.00
= $10.10
= $10.201
≈ $10.30
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Financial Functions
• Present Value (PV)
– What you get/pay at the beginning of the financial transaction
• Future Value (FV)
– What you are going to get OR what you will have to pay at the end
of the financial transaction
• Payment (PMT)
– Payment made each period. It remains constant over life of annuity
• RATE
– Interest rate per period
• NPER
– Number of payment periods
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Financial Functions-Syntax
=PV(rate, nper, pmt, [fv], [type])
=FV(rate, nper, pmt, [pv], [type])
=PMT(rate, nper, pv, [fv], [type])
=RATE(nper, pmt, pv, [fv], [type])
=NPER(rate, pmt, pv, [fv], [type])
NOTE: rate, nper, and pmt *must* be in the same unit in order
for the Excel calculations in the background to work correctly;
AND that unit must be the compound unit.
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Arguments in Financial Functions
Argument Description
rate
Interest rate per
compounding period
nper
Number of compounding
periods
pmt
Periodic payments to the
initial sum
pv
Original value of financial
transaction
fv
Value at the end of the
financial transaction
type
Designates when payments
are made
Argument Rules
Payment amount cannot vary
0: Payments are made at the end of the
period
1: Payments are made at the beginning of
the period
(0 is the default and is implied)
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Using Financial Functions Arguments
• Use consistent signs
– Outgoing cash ( - )
– Incoming cash ( + )
• For arguments that are zero, at least a comma must be put
in the function to maintain the argument order, unless no
other non-zero arguments follow.
=PV(.03, 2, 0, 5000, 0)
same as
=PV(.03, 2, , 5000)
11
Write an excel formula in cell D2 to calculate the payment for a loan
amount of $15,000 at 9% interest rate for a period of 5 years.
Assume the loan is compounded monthly.
=PMT(rate, nper, pv, [fv], [type]) ----Returns periodic payment
=PMT(.09/12,5*12,15000,0,0) OR =PMT(.09/12,5*12,15000)
12
Write an excel formula in cell B2 to determine how many years it
will take to save $12,000 if you put $10,000 into a savings account
paying 4% annual interest compounded quarterly.
=NPER(rate, pmt, pv, [fv], [type]) ----Returns # of Payment periods
=NPER(.04/4,0,-10000,12000,0) /4 OR =NPER(.04/4,,-10000,12000)/4
Note: Divide the function by the number of compounding
periods to calculate the number of years for the annuity
13
Write an excel formula in cell A2 to calculate the annual interest rate of a
new Chevy Cruz. The cost of the car is $18,999, and you will put down
$2,000. You will pay $350 per month for five years. The annual interest
rate is compounded monthly.
=RATE(nper, pmt, pv, [fv], [type]) ----Returns the rate per period
=RATE(5*12,-350,16999,0,0)*12 OR =RATE(5*12,-350,16999)*12
Note: Multiply the function by the number of compounding
periods to calculate the annual interest rate
14
Write an excel formula in cell E2 to determine how much money you
would have to put into a CD now to have a $5,000 down payment on a car
when you graduate in 2 years. The CD pays 3% annual interest rate
compounded yearly.
=PV(rate, nper, pmt, [fv], [type]) - Returns the present value of an investment
=PV(.03,2,0,5000,0) OR =PV(.03,2,,5000)
15
Write an excel formula in cell F2 to determine the value of a CD in 2 years.
You plan on an initial investment of $5,000 and you will add an additional $50
per month. The CD pays an annual interest rate of 3% compounded monthly.
=FV(rate, nper, pmt, [pv], [type]) - Returns the future value of an investment
=FV(.03/12,2*12,-50,-5000,0) OR =FV(.03/12,2*12,-50,-5000)
16
Write an Excel formula in cell G2 to calculate the monthly mortgage payment for a
$100,000 home with a balloon payment of $10,000. The annual interest rate is 4%
compounded monthly with a loan duration of 30 years. Note: A balloon payment is an
amount due at the end of the loan and is indicated in the fv argument as a negative value
.
17
Five years ago you won $75,000 on the game show, “I Wanna Win A lot of
Money”! At that time, you invested the money in a CD that paid 6% per year
compounded monthly. Write a formula in cell C9, to determine T/F if you have
enough money to purchase a $100,000 house without financing.
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