# Question

A few years back, Dave and Jana bought a new home. They borrowed $230,415 at a fixed rate of 5.49% (15-year term) with monthly payments of $1,881.46. They just made their twenty-fifth 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, 3.8%, 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 = the interest rate for the loan

nper = the total number of payments

pv = present value—the amount borrowed

fv = future value—the desired cash balance after the last payment (usually 0)

type = payment type (0 = end of period, 1 = beginning of the period)

For example, for the Dave and Jana’s original loan there will be 180 payments (12*15 = 180), so we would use =PMT(.0549/12,180,230415,0,0) = $1881.46. 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 today’s dollars. The formula for converting K dollars saved t months from now to today’s dollars is:

K / (1 + r)t-1

where r is the monthly inflation rate. Assume r = .002.

Use your model to get the savings in today’s dollars associated with the refinanced loan versus staying with the original loan.

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, 3.8%, 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 = the interest rate for the loan

nper = the total number of payments

pv = present value—the amount borrowed

fv = future value—the desired cash balance after the last payment (usually 0)

type = payment type (0 = end of period, 1 = beginning of the period)

For example, for the Dave and Jana’s original loan there will be 180 payments (12*15 = 180), so we would use =PMT(.0549/12,180,230415,0,0) = $1881.46. 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 today’s dollars. The formula for converting K dollars saved t months from now to today’s dollars is:

K / (1 + r)t-1

where r is the monthly inflation rate. Assume r = .002.

Use your model to get the savings in today’s dollars associated with the refinanced loan versus staying with the original loan.

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