The effective interest rate provides a true indication of the interest rate on loans that are progressively being reduced.

Effective Interest Rate Use

The effective interest rate is used to directly compare with the compounding interest rate as they both take into account the reduction of the principal amount.

The Rule

There are two ways to find the effective rate of interest- estimation and calculation.

• Estimation: A little less than $2\times$ flat interest rate
• Calculation: $\frac {2n}{n+1}\times$ flat interest rate

The flat rate is closest to being a true indication of the rate charged with fewer payments.

Example 1

Jake takes out a \$2,000 loan to pay for new furniture. The terms of the loan include equal quarterly repayments over two years at a simple interest rate of 9.2% p.a. Calculate the effective rate of interest to one decimal place.

Note the flat rate and number of instalments.

Flat rate $=9.2$
$n=2\times 4=8$

We are asked to calculate and need to provide a precise answer. Use the formula and substitute the known values.

Effective rate $=\frac {2n}{n+1}\times$ flat rate
Effective rate $=\frac {2\times 8}{8+1}\times 9.2$
Effective rate $=16.3555$

The effective rate of interest is 16.36% p.a.

Example 2

A flat interest rate of 6.4% p.a. is charged on a hire purchase with monthly repayments over two years. What is the effective interest rate?

a) 6.4% p.a.
b) 12.6% p.a.
c) 12.8% p.a.
d) 16.8% p.a.

This is a multiple choice question so we can estimate. We know that the effective interest rate should be a little less than two times the flat rate.

$2\times 6.4=12.8$

Remember, it is a little less than two times the flat rate so option b (12.6% p.a.) is correct.

Be Careful

An effective interest rate is different to a flat interest rate; the flat rate does not take into account the reductions in the balance owing after repayments are made.