Sharon will borrow $3400 at 11% APR. She will pay it back over 18 months. What will her monthly payment be? (Use The Table)
A) $ 512.42
B) $ 220.06
C) $ 681.50 D)$ 220.06
You are asked to do the same thing in this question, but the Table you are given is for interest only.
The way they have calculated it, per $100, is as follows: $100 x 11% x 18 months/12 months=$100 x 0.11 x 1.5 years =$16.50 as you can see from the Table under 11% and across 18 months.
Then, they want you to calculate it for $3,400. So, what you are supposed to do is the following:
$3,400/$100 x $16.50/18 =$31.17 - This is the monthly interest on $3,400, which is calculated INCORRECTLY!!!.
Then, they want you to take $3,400 / 18 months =$188.89 of principal per month. Then you add this to the monthly interest of $31.17. So, $188.89+$31.17 =$220.06 - which is one of the "answers" given to you, which is INCORRECT. If you accept this payment, then the interest rate would have to be 19.92% compounded monthly.
The correct monthly payment can be calculated using the following formula:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
PMT=$3,400 x 0.11/12{[1 + 0.11/12]^18 / [1 + 0.11/12]^18 - 1}
PMT=$31.16667 x {[1.0091667]^18 / [1.0091667]^18 - 1}
PMT=$31.16667 x {[1.1785069491] / [0.1785069491]}
PMT=$31.16667 x 6.60202280493......
PMT=$205.76 - This is the accurate monthly payment for the $3,400 Loan @ 11% compounded monthly over a period of 18 months.
