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 $65$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 $(0=$ end of period, $1=$ beginning of the period$)$ For example,

for Dave and Jana$$s original loan, there will be $180$ payments

$(12*15=180),$ so we would use $=$PMT$(0\mathrm{.}0549/12,180,230415,0,0)=$

$$1,881\mathrm{.}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:k$/(1+$r$)^$t$-1$where r is the monthly inflation rate. Assume that r $=0\mathrm{.}002$ 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. If

required, round your answer to the nearest whole dollar amount. If

your answer is negative use $$minus sign$.$