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 to the nearest tenth of a percent.

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 to the nearest tenth of a percent.

P​ = ​$2300.00​, A​ = ​$2328.75​, t​ = 3 months

________​% ​(Round to the nearest tenth of a​ percent.)

Answer 1

The simple interest formula is as follows: A = P (1 + rt), where "a" is the amount after "t" years and "r" is the interest rate.

Therefore, you are given P, A, and t, however t is given is months. So 3 months would be 1/4 year.

If we substitute we get:

2328.75 = 2300 (1 + r(1/4)) now we solve for "r".

/2300 /2300

1.0125 = 1 + (r/4)

-1 -1

.0125 = r/4

*4 *4

r = .05 or 5%

Note: if the answer was to be found in terms of monthly interest rate, simply change use t=3 instead.