Two years ago you signed a $4-$year lease on a DeLorean DMC$-12.$ The sticker price on the car was

$$39,952\mathrm{.}61,$ the lease rate was $3\%,$ and the monthly payments $($starting at the time of signing$)$ were

$$530.$ The buyout was $$17,978\mathrm{.}68$ due at the end of the lease term. Now $($two years after signing the

lease but just before the $25$th lease payment$)$ DeLorean has just released the new DMC$-13$ with

better styling and $20\%$ more horsepower. You want to get out of your lease on the old car and lease

one of the new ones. DeLorean is happy to take your car from you and cancel the lease if you have

positive equity in the car. That is$,$ if the resale value of the car exceeds the principal sill owing $($the

difference is positive equity$).$ However, if the resale value is less than the principal outstanding,

DeLorean will require you to pay the difference in order to exit the lease. The resale value of the old

DeLorean is $$29,794\mathrm{.}75.$ What is the value of your equity in the car?