Introduction to Corporate Finance

PART 1: INTRODUCTION

As usual, Excel provides a shortcut for this calculation in the form of the payment PMT (payment)

function. The syntax of this function is = pmt(rate,nper,pv,fv,type). To solve this particular problem using

the PMT (payment) function, you would enter =pmt(0.06,5,0,20,000,0), and Excel generates the result

$3,547.93. Notice that in this function you enter 0 for the present value because you start with nothing

saved toward the down payment. Also, the value entered for ‘type’ is 0 because this is an ordinary annuity –

you are making equal end-of-year deposits to achieve your goal. Alternatively, you can use a financial

calculator to find the answer as shown below.

Formula B4: =PMT(B3,B2,0,B1)

Payment $3,547.93

Interest rate 6%

5

–$20,000

Number of periods

Future value

Input

Solution

–20,000

5

6

FV

N

I

CPT

PMT

3,547.93

Function

Row

Column

Calculator Spreadsheet

1

2

3

4

5

A B

3 -7d LOAN AMORTISATION

Loan amortisation refers to a situation in which a borrower pays down the principal (the amount borrowed)

on a loan over the life of the loan. Often, the borrower makes equal periodic payments. For instance, with

a conventional, 30-year home mortgage, the borrower makes the same payment each month for 30 years

until the mortgage is completely repaid. To amortise a loan (that is, to calculate the periodic payment

that pays off the loan), you must know the total amount of the loan (the amount borrowed), the term of

the loan, the frequency of periodic payments and the interest rate.

In terms of the time value of money, the loan amortisation process involves finding a level stream

of payments (over the term of the loan) with a present value (calculated at the loan interest rate) equal

to the amount borrowed. Lenders use a loan amortisation schedule to determine these payments and the

allocation of each payment to interest and principal.

loan amortisation
Occurs when a borrower pays
back the principal over the
life of the loan, often in equal
periodic payments

loan amortisation
schedule
Used to determine loan
amortisation payments
and the allocation of each
payment to interest and
principal

As a demonstration of this formula, you would need to make equal annual end-of-year deposits of $3,547.93

each year to accumulate $20,000 (the FV) at the end of five years (n = 5), given an interest rate of 6% (r = 6%):

PMT

$20,000

[(1.06)1]

0.06

= 5 $3,547.93

 −











=

example