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.