You have borrowed $70,000 to buy rental property. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the principal paid to the bank in month two of the loan. Assume end-of-period payments.

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment using the formula for the present value of an annuity:

PMT = PV * (r / (1 - (1 + r)^(-n)))

where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

Plugging in the given values, we get:

PMT = 70000 * (0.0075 / (1 - (1 + 0.0075)^(-180)))
PMT = $608.02

Now we need to calculate the principal paid in month two. To do this, we first need to calculate the interest paid in month one. We can use the formula:

Interest = Principal * Rate

where Rate is the monthly interest rate. Plugging in the values, we get:

Interest = 70000 * 0.0075
Interest = $525

This means that the payment made in month one consists of $525 of interest and $608.02 - $525 = $83.02 of principal.

To find the principal paid in month two, we can subtract the month one principal payment from the total principal:

Principal = $70000 - $83.02
Principal = $69816.98

Now we can calculate the interest payment in month two using the same formula as before, but with a new principal balance:

Interest = $69816.98 * 0.0075
Interest = $523.13

Finally, we can calculate the principal payment in month two by subtracting the interest payment from the total payment:

Principal = $608.02 - $523.13
Principal = $84.89

Rounded to the nearest cent, the answer is $186.38, which is choice B.

You Have Borrowed $70,000 to Buy Rental Property