Consider again the mortgage refinance problem faced by Dave and Jana in Problem 16. Assume that they have accepted the refinance offer of a 15-year loan at 3 percent interest rate with out-of-pocket expenses of $2,937. Recall that they are borrowing $208,555.87. Assume there is no prepayment penalty, so that any amount over the required payment is applied to the principle. Construct a model so that you can use Goal Seek to determine the monthly payment that will allow Dave and Jana to pay off the loan in 12 years. Do the same for 10 and 11 years. Which option for prepayment, if any, would you choose and why? Recall that the monthly interest that is charged is the monthly loan rate multiplied by the remaining loan balance.
A few years back, Dave and Jana bought a new home. They borrowed $230,415 at an annual fixed rate of 5.49 percent (15-year term) with monthly payments of $1,881.46. They just made their 25th payment, and the current balance on the loan is $208,555.87. Interest rates are at an all-time low, and Dave and Jana are thinking of refinancing to a new 15-year fixed loan. Their bank has made the following offer: 15-year term, 3.0 percent, plus out-of-pocket costs of $2,937. The out-of-pocket costs must be paid in full at the time of refinancing. Build a spreadsheet model to evaluate this offer. The Excel function
=PMT(rate, nper, pv, fv, type)
calculates the payment for a loan based on constant payments and a constant interest rate. The arguments of this function are rate 5 the interest rate for the loan nper 5 the total number of payments pv 5 present value (the amount borrowed) fv 5 future value [the desired cash balance after the last payment (usually 0)] type 5 payment type (0 5 end of period, 1 5 beginning of the period) For example, for Dave and Jana’s original loan, there will be 180 payments (12*15 5 180), so we would use 5PMT(0.0549/12, 180, 230415,0,0) 5 $1,881.46. Note that because
payments are made monthly, the annual interest rate must be expressed as a monthly rate. Also, for payment calculations, we assume that the payment is made at the end of the month. The savings from refinancing occur over time, and therefore need to be discounted back to current dollars. The formula for converting K dollars saved t months from now to current dollars is
where r is the monthly inflation rate. Assume that r 5 0.002 and that Dave and Jana make their payment at the end of each month. Use your model to calculate the savings in current dollars associated with the refinanced loan versus staying with the original loan.
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