Final answer:
Eponine's monthly mortgage payment on a $300,000 loan at 5.5% APR over 30 years is approximately $1,703.37 when calculated exactly with the standard mortgage formula. The closest given option is B) $1,650, but none of the options provided match the calculated payment exactly.
Step-by-step explanation:
To calculate Eponine's monthly mortgage payment, we use the formula for a fixed-rate mortgage which is:
M = P[i(1+i)^n]/[(1+i)^n - 1],
where M is the monthly payment, P is the principal amount ($300,000 in this case), i is the monthly interest rate (APR divided by 12 months), and n is the total number of payments (360 for a 30 year mortgage).
First we need to find the monthly interest rate: i = 5.5% / 12 = 0.0045833.
Now plug in the values into the formula:
M = 300,000[0.0045833(1+0.0045833)^360]/[(1+0.0045833)^360 - 1]
Calculating the above expression using a calculator, we find that the monthly payment M comes out to be approximately $1,703.37, when rounded to the nearest dollar.
Comparing this with the options provided, although none of them match correctly, Option B) $1,650 is the closest. This discrepancy might be due to rounding differences or a typo in the options presented. However, based on the calculation, the monthly payment would be slightly higher at approximately $1,703.37.