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# Hard Financial Problem.

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A new car valued at \$27,500 is to be leased for 3 years, or 36 months @ \$516.60 in advance, per month. The lessee has the option to purchase the car for \$15,500 at the end of the leasing period. If the lessee purchases the car at the end of the lease, what is the return, compounded monthly, to the car dealership? Thanks for help.

Jul 19, 2017

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Find the FV of the \$27,500 @ a given rate such as 12% compounded monthly...................(1)
Then find the FV of the 36 monthly payments of \$516.60 @ the same given rate of 12% C.M..........(2)
Subtract (2) from (1) above and the result should be as close to \$15,500 as possible. Iterate (1) and (2) above to get as close as possible to \$15,500. That interest rate, compounded monthly, would be the return to the car dealership. This is how it would be calculated manually to get the answer.
However, we are going to use this fine online calculator to find the rate directly. We enter -\$27,500 under PV. Notice that we enter it as a negative amount because it is money "owed" from the point of view of the car dealership. Then we enter \$15,500 under FV, \$516.60 under PMT, and 36 under NP, or number of payments. We choose the "beginning" mode since the lease payments are paid in advance or at the beginning of the month. Then we simply press "IR", or interest rate. It will give us the interest rate "per period", or in this case "per month". Then, we simply multiply it by 12 to give us annual rate compounded monthly.
We find that the calculator gives a monthly rate of 0.854169 x 12 =10.25% compounded monthly. Here is the financial calculator:
https://arachnoid.com/finance/index.html?pv=0&fv=100000&np=200&ir=1&pb=false

Jul 20, 2017