PART 1: INTRODUCTION

To find the annual payment required on the five-

year, $25,000 loan with an 8% annual interest rate,

we substitute the known values of PV = $25,000,

r = 0.08 and n = 5 into the right-hand side of the

equation:

PMT

$25, 000

1

0.08

1

1

(0.08)

$6,261.41

5

=

×−























=

Five annual payments of $6,261.41 are needed

to fully amortise this $25,000 loan. We could also

solve this problem using Excel’s payment function.

This time, the present value is $25,000, and we want

the future value to be $0 (that is, the loan balance

in five years should be $0). In Excel, you could enter

=pmt(0.08,5,25,000,0,0), and you would obtain the

same answer, $6,261.41. Finally, this problem could

be solved using a financial calculator, as shown below.

example

Formula B4: =PMT(B3,B2,B1)

Payment $6,261.41

Interest rate 8%

5

–$25,000

Number of periods

Present value

Input

Solution

–25,000

5

8

PV

N

I

CPT

PMT

6,261.41

Function

Row

Column

Calculator Spreadsheet

1

2

3

4

5

A B

14 Why is the effective annual rate often greater than the stated annual rate?

15 On a 30-year mortgage, would the total amount of money paid by the borrower over the life of the

loan be greater if there were weekly payments or monthly payments?

Earlier, we found the present value (PV) of an n-year ordinary annuity, using Equation 3.7. Solving

that equation for PMT, the annual loan payment, we get Equation 3.16:

Eq. 3.16 (^) PMT
PV
rr

1
1
1
(1+)n
×−












Each loan payment consists partly of interest and partly of the loan principal. Columns 3 and 4 of the loan
amortisation schedule in Table 3.3 show the allocation of each loan payment of $6,261.41 to interest and principal.
Observe that the portion of each payment representing interest (column 3) declines over the repayment period, and
the portion going to principal (column 4) increases. This pattern is typical of amortised loans. With level payments,
the interest component declines and a larger portion of each subsequent payment is left to repay principal.
Computing amortised loan payments is the present value formulation that people use most frequently in
their personal lives to calculate car loan and home mortgage payments. Because lenders typically require monthly
CONCEPT REVIEW QUESTIONS 3-7