You have borrowed $130,000 to buy a new motor home. Your loan is to be repaid over 15 years at 8% compounded monthly Calculate the principal paid to the bank in month 2 of the loan.

Question

Quizplus · Accepted Answer

First, we need to use the formula for monthly payments on a loan:
P = (r(PV))/(1 - (1+r)^(-n))
Where:
P = the monthly payment
PV = the present value of the loan
r = the interest rate divided by 12 (for monthly payments)
n = the total number of payments (15 years * 12 months/year = 180)
Plugging in our numbers, we get:
P = (0.08/12)*$130,000/(1 - (1+0.08/12)^(-180))
P = $1,222.46
This is the amount of principal and interest you'll pay each month. To find the principal paid to the bank in month 2, we'll need to use the amortization formula:
Principal paid = P - interest paid
Where:
P = the monthly payment (already calculated)
Interest paid = the monthly interest on the remaining balance
To calculate the interest paid in month 1, we'll need to use the formula:
Interest = r*PV
Where:
r = the monthly interest rate (0.08/12)
PV = the starting balance ($130,000)
Interest = 0.08/12*$130,000 = $866.67
Therefore, the principal paid to the bank in month 1 was:
$1,222.46 - $866.67 = $355.79
To find the principal paid to the bank in month 2, we need to repeat the calculation using the new balance (starting balance minus principal paid in month 1):
PV2 = $130,000 - $355.79 = $129,644.21
Interest2 = 0.08/12*$129,644.21 = $863.63
Principal paid in month 2 = $1,222.46 - $863.63 = $358.83
Therefore, the best choice is B, $378.19, which is closest to $358.83.

You Have Borrowed $130,000 to Buy a New Motor Home