Answer:
a) $1392
b) 2 years, 8 months
c) $1474.10
Explanation:
You want the monthly payments on a 3-year $47,500 loan at 3.5% compounded semi-annually. When the payments are $1542, you want the payoff time and the amount of the final payment.
Compounding
Usually interest is compounded at the same frequency as the payments. When payments are paid monthly and compounding is semi-annual, the calculation can be a bit tricky. Here, we let a calculator figure it out. We expect the calculation is accomplished by translating the effective annual interest rate to an effective monthly rate. That monthly rate will be ...
(1 +0.035/2)^(1/6) -1 = 0.289562% per month, an APR of about 3.4747%
a) Monthly payments
The calculator tells us the monthly payments will be $1392.
b) Payoff time
With monthly payments of $1542, the calculator tells us the payoff time will be 32 months, about 2 years, 8 months.
c) Final payment
Paying 1542 for 32 months will result in an overpayment of $67.90, so the final payment will be less by this amount.
The final payment is $1474.10.
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