# Chapter 6

```Agenda 11/28
 Review Quiz 4
 Discuss interest and the time value of money
 Explore the Excel time value of money functions
 Examine the accounting measures of profitability
 Course Evaluations
Introduction to Interest Calculations
 When you borrow money you pay interest
 When you loan money, you receive interest
 When you make a payment
 part of the payment is applied to interest
 Part of the payment is applied to principal
Understanding time value of money
3
 Money will increase value over time if the money is
invested and can make more money.
 If you have \$1,000 today, it will be worth more
tomorrow if you invest that \$1,000 and it earns
additional money (interest or some other return on
that investment).
 If you have \$1,000 today, it will NOT be worth more
tomorrow if you put it in an envelope and hide it in a
drawer. Then the time value of money does not
apply. Of course, you won’t lose the \$1,000 either…
Types of Interest
 Simple interest
 Interest is paid only on the principal
 Many certificates of deposit work this way
 Compound interest
 Interest is added to the principal each period
 Interest is calculated on the principal plus any accrued interest
 Compounding can occur on different periods

Annually, quarterly, monthly, daily
Difference between simple and compound interest
5
 Assume that you have \$1,000 to invest. \$1,000 is
the present value (PV) of your money.
 You can invest it and receive “simple” interest or you
can earn “compound” interest.
 The money that you have at the end of the time you
have invested it is called the “future value” (FV) of
Future value of money
6
 Simple interest is always calculated on the initial
\$1,000. 5% interest on \$1,000 is \$50. Always \$50.
 When interest is paid on not only the principal
amount invested, but also on any previous interest
earned, this is called compound interest.
FV = Principal + (Principal x Interest)
= 1000 + (1000 x .05)
= 1000 (1 + i)
= PV (1 + i)
Simple vs. compound
interest
comparison
7
Year
Simple Interest
Compound Interest
0
\$1,000
\$1,000
1
\$1,050
\$1,050
2
\$1,100
\$1,102.50
3
\$1,150
\$1,157.62
4
\$1,200
\$1,215.61
5
\$1,250
\$1,276.28
10
\$1,500
\$1,628.89
20
\$2,000
\$2,653.30
30
\$2,500
\$4,321.94
\$1,000 Invested at 5% return
What about if you borrow money?
8
 If you borrow money, the lender wants to earn
“compound” money on its investment.
 If you borrow \$1000 at 10%, then you won’t pay back
just \$1,100 (unless you pay it back at once during the
initial time period).
 You will pay it back “compounded”. Interest will be
calculated each period on your remaining balance.
Amortization table \$1,000 loan, pay \$200 year, 10% year
interest
9
Year
Amount Owed
Amount Plus
Interest
Payment
1
\$1,000.00
\$1,100.00
\$200.00
2
\$900.00
\$990.00
\$200.00
3
\$790.00
\$869.00
\$200.00
4
\$669.00
\$735.90
\$200.00
5
\$535.90
\$589.49
\$200.00
6
\$389.49
\$428.44
\$200.00
7
\$228.44
\$251.28
\$200.00
8
\$51.28
\$56.41
\$56.41
Total Paid
\$1,456.41
Types of financial questions usually asked
10
 How much will it cost each month to pay off a loan if
I want to borrow \$150,000 at 6% interest each year
for 30 years?
 Assume that you need to have exactly \$40,000 saved
10 years from now. How much must you deposit
today in an account that pays 6% interest,
compounded annually, so that you reach your goal of
\$40,000?
 If you invest \$2,000 today and have accumulated
\$2,676.45 after exactly five years, what rate of
annual compound interest was earned?
Some Excel financial functions
Function
Description
CUMIPMT
Cumulative Interest Payments
CUMPRINC Cumulative Principal Payments
FV
Future Value
IPMT
Interest Payment
IRR
Internal Rate of Return
NPER
Number of periods
NPV
Net Present Value
PMT
Payment
PPMT
Principal Payment
PV
Present Value
RATE
Interest Rate
SLN
Straight Line Depreciation
11
The PMT Function (Introduction)
 PMT is used to calculate the periodic payment on a
loan
 The interest rate must be fixed
 There may be a residual value on the note at the end
of the periods


This is often referred to as a balloon payment
An auto lease, for example, would have a residual note value
The PMT Function (Arguments 1)
 Rate: The first argument contains the interest rate per
compounding period
 Nper: The second argument contains the number of periods
 PV: The third argument contains the present loan value
 FV: The fourth argument contains the future value

If the loan is paid off at the end of the periods, the value is 0
 Type: The final argument indicates when payments are made


0 (the default) indicates the end of the period
1 indicates the beginning of the period
The PMT Function (Arguments 2)
The PMT Function (Example)
Other Time Value of Money Functions
 Here we are just solving the same equation for a
different variable





RATE determines the interest rate
NPER determines the number of periods
PMT determines the payment
PV determines the present value of a transaction
FV determines the future value of a transaction
The RATE Function (Introduction)
 Determines the interest rate per period based on
 The number of periods
 The payment
 The present value
 The future value
 The type
The RATE Function (Arguments)
The RATE Function (Example)
The NPER Function (Introduction)
 Determines the number of periods based on
 The interest rate
 The payment
 The present value
 The future value
 The type
The NPER Function (Arguments)
The NPER Function (Example)
The FV Function (Introduction)
 Determines the future value of a lump sum
 It’s possible for FV to account for regular cash flows (periodic
payments) per period
The FV Function (Arguments)
The FV Function (Example)
The PV Function (Introduction)
 Determines the present value of a cash flow
 Like FV, regular inflows or outflows are supported
THE PV Function (Arguments)
The PV Function (Example)
The IPMT Function (Introduction)
 Use IPMT to calculate the interest applicable to a
particular period

Use the initial balance for the present value no matter the
period
 Use PPMT to calculate the principal applicable to a
particular period
 The arguments to both functions are the same
The IPMT Function (Arguments)
The CUMIPMT Function (Introduction)
 CUMIPMT calculates the cumulative interest between
two periods
 CUMPRINC calculates the cumulative principal
between two periods
 The arguments to both functions are the same
 Functions require the analysis tool pack add-in
The CUMIPMT Function (Arguments)
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