A new car valued at $23,500 is to be leased for 3 years. The lessee has the option to purchase the car for $17,500 at the end of the leasing period. What monthly payments, with one payment in advance, are necessary to yield the lessor 14% compounded annually? Calculate the payments from the lessor’s point of view. Thanks for any help.
A new car valued at $23,500 is to be leased for 3 years. The lessee has the option to purchase the car for $17,500 at the end of the leasing period. What monthly payments, with one payment in advance, are necessary to yield the lessor 14% compounded annually? Calculate the payments from the lessor’s point of view. Thanks for any help.
This financial calculation can be done in a number of ways. The easiest way to solve it is to use a TVM formula to calculate the payment directly:
Since they want monthly payments, we have to convert 14% comp. annually to comp. monthly, which comes to=13.1746223402/12=1.09788519502 per month.
The formula in question for this particular problem is:
-P*[(1-(1+R/100)^-N)/(R/100)]+FV*(1+(R/100))^-N-PV=0, Where R=Interest rate per period, N=number of periods, P=periodic payment, PV=Present value, FV=Future value.
By substituting in the above equation, we solve directly for P=payment.
-P*[(1-(1+.0109788519502)^-36)/(.0109788519502)]+17,500*(1+(.0109788519502))^-36-23,500=0
Using Wolfram/Alpha engine to expedite caculation, it gives P=$394.80, which is at the end of month:
We simply divide it by 1.0109788519502 to get =$390.51 for the beginning of the month.
P.S. I have calculated it in two other ways and they all agree.
Thank you very much for this. But where did you get that big scary equation from? I have never seen it before.
That is an equation that combines FV, PV and PMT formulas into one "Master Equation", as it is known in the Investment Community. The advantages of this equation is that if you know four variables, it can solve directly for the fifth. It may look complicated and "scary", but is in fact very simple and straightforward. It saves quite a bit of time. You can copy it and use it in the future.
