The Fairfold family decided to buy a super ski and water sports boat. They took out an $80,000, 5-year, 6% per year, compounded semiannually loan with monthly payments from First Bank and Trust (FB&T). After making only two payments, a banker friend offered to make them a better deal: a 5?year, 4.2% per year, compounded semiannually loan with no transfer fee to his bank and a complete repayment no-fee-required of the remaining principal to FB&T. The principal on the new loan will be the remaining principal from the current loan. Answer the following questions for the Fairfolds as they deliberate this new offer.
(a) What is the current monthly payment on the $80,000 loan?
(b) What is the current principal due on the current loan?
(c) How much interest have they already paid in the first two payments?
(d) What is the amount of the new monthly payment starting with month 3, if the new loan offer is accepted?
PP = month; CP = month; use i = 0.005 per month
(a) A = 80,000(A/P,0.5%,60) = 80,000(0.01933) = $1546.40 per month
(b) Current principal balance is $77,701.47 (see table below)
(c) Sum of interest paid: 400.00 + 394.27 = $794.27
(d) Now i = 0.042/12 = 0.0035 per month
A = 77,701.47(A/P,0.35%,60) = 77,701.47(0.01851) = $1438.25 per month
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