Hint$($s$)$ Check My Work

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A few years back, Dave and Jana bought a new home. They borrowed $$230,415$ at an annual fixed rate of $5\mathrm{.}49\%(15-$year term$)$ with monthly payments of $$1,881\mathrm{.}46.$ They just made their $40$ th payment, and the current balance on the loan is $$208,555\mathrm{.}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, $3\mathrm{.}0\%,$ 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 end of period, $1=$ beginning of the period