*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 flat interest rate
- Calculation: 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

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

Effective rate flat rate

Effective rate

Effective rate

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.

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.

#### See also

Simple Interest

Hire Purchase

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