Please help me on this question

Question

Alan writes the equation A=500(1.25)^t to figure out how much it will cost him for a one-year loan of  $500 with an interest rate of 25% compounded only once. He wants to determine the annual percentage rate (APR) for a loan that would cost the same amount overall, if it is compounded monthly, instead of only once.

Which equation should he use, and what is the APR?

1. A≈500(1.0188)^12t APR≈22.56%
2. A≈500(1.25)^12t APR≈1.88%
3. A≈500(1.25^12)^1/12t APR≈14.55%
4. A≈500(1.0188)^12t APR≈1.88%

Answer 1

for one year, at simple interest, it costs him 25% of $500 = $125 interest

for compounded 12 times,

A = 500(1+ r/12)^12 =625 where r = 0.0188

=500(1.0188)^12 = about 500(1.25) = 625

the first choice is correct.

simple annual interest at 25% is equivalent to 22.56% annual interest compounded monthly.

both require $125 interest

r/12 = .0188 = 1.88%

r = 12(.0188) = .2256 = 22.56% annual rate of interest