Question

Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.

Answer 1

Using simple interest, it is found that the APR is of 4.472%.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

$A(t) = A(0)(1 + rt)$

In which:

• A(0) is the initial amount.

• r is the interest rate, as a decimal.

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

$A(t) = A(0)(1 + rt)$

$3067.08 = 3000(1 + 0.5r)$

$1 + 0.5r = \frac{3067.08}{3000}$

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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