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Billy takes out a $2,400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate? Give your answer as a percentage to the nearest tenth of a percent. Do not include the percent symbol in your answer.



Answer :

To calculate the total interest payable, we use the formula

I=Prt

where:

I = simple interest

P = $2,400

r = 0.08

t = 18/12

Then I = 2,400 x 0.08 x 1.5 = 288

Therefore the total amount he receives at loan drawdown is $2,400 − $288 =$2,112.

Now to calculate the effective interest rate we use the formula

A=P(1+rext).

where

A = $2,400

P = $2,112

t = 1.5

re = effective interest rate

so we have: 2,400 = 2,112(1 + 1.5xre)

finally we solve for re and we obtain

re = 9.1

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