math problem in description

Question

melissa took out a 9000 loan for 7 months and was charged simple interest. the total interest she paid on the loan was $336. as a per what was the annual interest rate of melissas loan? DO NOT round to any intermediate computations

Answer 1

7/12 x 9000 x r = 336, where r= APR = annual rate of interest

r = 336(12/7(9000)=4032/63000 = .064 = 6.4%

annual rate = interest times number of years (or part of a year) divided by the loan amount

if it's simple interest, with no compounding. A much simpler problem with simple interest. complexity compounds with compound interest, although compound interest is a more interesting problem. More interest with compound interest.

Answer 2

The formula for simple interest is I = prt, and in this question, you are given the principal, time, and interest. The interest rate (r) is the unknown factor you are trying to find.

I = 336 (the amount of interest paid on the principal amount)

p = 9000 (principal amount that was paid up front)

r = ? (annual interest rate)

t = 7/12 (time in terms or years; since time is 7 months, 7/12 means 7 months out of the 12 months in a year)

In order to find the annual interest rate (r), you need to get "r" by itself. To do that, divide both sides of the simple interest formula by "pt," to cancel out the "p" and the "t" on the right side of the equation.

I/pt = prt/pt

I/pt = r

Now that "r" is by itself, plug in the numbers given in the question to find interest rate.

336/(9000(7/12)) = r

336/5250 = r

0.064 = r

To change the annual interest rate to its percent form, multiply "r" by 100.

0.064(100)

6.4%

The annual interest rate is 6.4%

To check your work, substitute your answer into the interest formula to see if the equation is true.

I = prt

336 = 9000(0.064)(7/12)

336 = 336 [true]