Question

You take out a 2-year, $5,000 loan at 7% simple annual interest. The lender charges you a $300 fee. Thinking of the fee as additional interest, what is the actual annual interest rate you will pay? Round answer to the nearest 0.001%.

Answer 1

First we will calculate the simple interest for 2 years as per below:

Simple interest = P * r * n

where, P = Principal amount = $5000, r = rate of interest = 7% and n is time period = 2

Now, putting the values in the above formula, we get,

Simple interest = $5000 * 7% * 2

Simple interest = $700

Additional interest = Fee = $300

Total interest = $700 + $300 = $1000

Now, we will calculate annual interest rate by the simple interest formula with the below figures:

P = $5000, Simple or total interest = $1000, n = 2.

Now, simple interest formula is:

Simple interest = P * r * n

Putting the values in the above formula, we get,

$1000 = $5000 * r * 2

$1000 = $10000 * r

r = $1000 / $10000

r = 0.1 or 10%