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 = P(r/n)/(1 - (1 + r/n)^(-nt))

Where:
PMT = monthly payment
P = principal amount borrowed
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = total number of years

Plugging in the given values, we get:

PMT = 70,000(0.09/12)/(1 - (1 + 0.09/12)^(-12*15))
PMT ≈ $675.87

Next, we need to calculate the principal and interest portions of the payment for month two. To do this, we can use the formula:

Principal paid = PMT - (previous balance x r/n)

Where:
previous balance = remaining balance from the previous month

For the first payment, the previous balance is simply the principal amount borrowed ($70,000). So the principal paid in month one is:

Principal paid = $675.87 - ($70,000 x 0.09/12)
Principal paid ≈ $610.43

Now, for month two, the previous balance is the remaining balance after the first payment, which is:

$70,000 - $610.43 = $69,389.57

So the principal paid in month two is:

Principal paid = $675.87 - ($69,389.57 x 0.09/12)
Principal paid ≈ $186.38

Therefore, the answer is B.

You Have Borrowed $70 000 to Buy Rental Property