Final answer:
Using the annuity payment formula, Megan's monthly payment for her $85,600 loan at a 11.5% interest rate, compounded monthly over twelve years, is determined to be $629.52.
Step-by-step explanation:
To determine Megan's monthly payment for her loan with an interest rate of 11.5%, compounded monthly, over twelve years, we can use the formula for the payment of an annuity which is given by:
PV = P * [ (1 - (1 + i)^-n) / i ]
Where:
- PV stands for the present value (or amount of the loan), which is $85,600
- P is the monthly payment
- i is the monthly interest rate (annual interest rate divided by 12)
- n is the total number of payments (months in this case)
Given that the loan term is 12 years or 144 months (12 months * 12 years) and the monthly interest rate is 11.5%/12 = 0.9583%, the formula rearranges to solve for P (monthly payment):
P = PV / [ (1 - (1 + i)^-n) / i ]
Plugging in the numbers:
P = 85600 / [ (1 - (1 + 0.009583)^-144) / 0.009583 ]
By calculating the above expression, we can find that the correct monthly payment Megan made is option b. $629.52.