You borrow $900 to buy a laptop. You plan to pay off the loan after 5 years of equal monthly payments. After 10 payments, you have $1200 left to pay. What is the simple annual interest rate of your loan?

The simple annual interest rate on my loan is 12%

Step-by-step explanation:

I planned to pay off the loan after 5 years of equal payments; There are 12 months that make up one year and the total number of months in five years = 12 × 5 = 60 months. This means that I planned to pay off the loan after 60 equal monthly payments.

If I have also made 10 of such monthly payments already and I have $1,200 left, it means that I now have 50 more months to clear the $1,200 that is left.

If I have $1,200 left to pay in 50 months, then my average payment per month is =

$1,200/50 = $24

Since I pay $24 monthly which includes part of the principal and the interest, then my total payment over the five years (60 months) will be = 24 × 60 = $1,440 (Principal+interest).

If the principal borrowed was $900, then the interest charged on the money over the 5 years = $1,440 - $900 = $540

With the interest known, we will now use the simple interest formula to find the simple annual interest rate on the loan.

Simple interest = (Principal×Rate×Time)/100

Where, S.I = $540

P = $900

T = 5years

R = ?%

540 = (900 × R × 5)/100

45R = 540

R = 540/45

R = 12%

Therefore, the simple annual interest rate on my loan is 12%

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