Question

The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r.

P = $2300, A = $2792, t = 9 months
The loan's simple interest is%.
(Round to the nearest tenth of a percent as needed.)

Answer 1

Probably the simplest approach to this problem is through the formula for simple interest:

I = Prt

You can plug in everything except r, which is the unknown.

The interest to be paid is the future value (A) minus the original loan value (P), so the interest to be paid is

2021.13 - 1900 = $121.13

The time (in years) is 9/12 or 0.75 year

Now plug in everything:

I = Prt

121.13 = 1900 x r x 0.75

121.13 = 1425r (multiplying 1900 x 0.75)

0.0850035 = r (dividing by 1425)

Converting the decimal to a percent and rounding gives 8.5% <--- ANS