© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Annual percentage rate with more than one instalment

Lower APR

It’s a bargain!

A few easy instalments.

Is this APR really correct?

APR with more than one instalment

This activity is about finding and checking APRs

For one instalment the loan is:

C = which gives the APR, i, as a decimal when a loan of £C is paid back by a single repayment £A after n years.

APR with more than one instalment

The general APR formula for cases involving more than one instalment is C =

m

ki

kA

kt1)1(

where i is the APR expressed as a decimal

ni1A

k is the number identifying a particular instalment

Ak is the amount of the instalment k

tk is the interval in years between the payment of the instalment and the start of the loan

When there are 4 annual instalments, A1, A2, A3 and A4 , the formula becomes

432 14

13

12

11

i

A

i

A

i

Ai

AC

Think aboutWhat is the formula for 3 annual instalments?

APR with more than one instalment

What is the formula for 5 annual instalments?

Reflect on your workWhy is it important to know the APR when a loan is repaid in several instalments?

What methods do you know for calculating the APR?

How would you set up a spreadsheet to carry out the calculations required by the interval bisection method?

APR with more than one instalment

Write down the formulae used when there is: 1 repayment, 2 repayments, and 3 repayments.