Your friend wants to start a new business. You agree to lend him $3500 at a simple interest rate of 2.5%. He writes you a check of $3718.75. How long in months did your friend have the loan?

Answer 1

Simple interest accrues on principal only. Therefore, the computation of simple interest is:

Interest = Principal x annual rate x months/12

In this case, you loaned your friend $3,500 but they repaid $3,718.75. The $3,718.75 included the $3,500, so they repaid $3,718.75 - $3,500, or $218.75, in interest.

Interest = Principal x annual rate x months/12

$218.75 = $3,500 x .025 x months/12

$218.75 = $87.50 x months/12

$2,625 = $87.50 x months

30 = months

The loan was outstanding for 30 months.