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 $25$ 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, $2\mathrm{.}25\%,$ plus out$-$of$-$pocket costs of

$$2,185.$ 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 as follows.

For example, for Dave and Jana's original loan, there will be $180$ payments $(12**15=180),$ so we would use $=$ PMT $(\frac{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

$\frac{K}{(1+r{)}^{t-1}}$

where $r$ is the monthly inflation rate. Assume that $r=0\mathrm{.}001$ 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. $($Round your answer the nearest cent.$)$

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