At the end of a 10-year loan, $13,570 had
been paid in interest. if the initial loan
amount was $23,000, find the interest rate.

5.9%

Step-by-step explanation:

Assuming simple interest compounded annually,

Final Amount = Initial amount [ 1 + (interest rate)(number of years) ]

or mathematically

A = P (1 + rt)

in our case, we are given

A = Initial Amount + Interest = $23,000 + $13,570 = $36,570

P = $23,000

t = 10 years

Substituting this into the equation for simple interest,

36,570 = 23,000 (1 + 10r)      (divide both sides by 23,000 and rearrange)

(1 + 10r) = 36,570 / 23,000

(1 + 10r) = 1.59   (subtract 1 from bot sides)

10r = 1.59 - 1

10r = 0.59  (divide both sides by 10)

r = 0.59 / 10

r = 0.059

hence the interest rate expressed as percentage is,

0.059 x 100% = 5.9%

it is a reproduction.

step-by-step explanation: