Question

Tim needs a new car while he attends college for the next three years. The car he would like has an MRSP of $15,000.local dealer can get him a three-year loan with a 7% interest rate if Tim can make a $1,500 down payment. The samedealer offers the same car for lease with a money factor of 0.00271 and a residual value of 75%. The lease requires anadditional fee of $1,250 to cover Tim's security deposit and the acquisition and documentation fees for the car. Tim islooking to drive the car home with the smallest monthly payment. Should he buy or lease the car. Show work.

Answer 1

To get the monthly payment from the parameter given, the formula below will be used

$\begin{gathered} M=\frac{P\times r}{1-(1+r)^{-n}} \\ M=\text{monthly payment; P=difference betw}een\text{ the down payment and the MRSP} \\ r=\text{rate; n=duration} \end{gathered}$$\begin{gathered} r=\frac{7}{100}\times\frac{1}{12}=\frac{0.07}{12}=0.006 \\ n=12\times3=36 \\ P=15000-1500=13500 \end{gathered}$

Substituting into the formula

$\begin{gathered} M=\frac{13500\times0.006}{1-(1+0.006)^{-36}} \\ M=\frac{81}{1-(1.006)^{-36}} \\ M=\frac{81}{1-0.8063} \\ M=\frac{81}{0.1937} \\ M=\text{ \ 418.17} \end{gathered}$

For the Leasing:

$\text{Finance cost =(Net Capitalized cost+Residual Value)}\times money\text{ factor}\times lease\text{ term}$$\begin{gathered} \text{Net Capitalized cost=15000-1500+1250=14750} \\ \text{ Residual value =0.75}\times15000=11250 \\ \text{money factor=0.00271} \\ \text{lease term=12}\times3=36 \end{gathered}$$\begin{gathered} \text{Depreciation cost=}\frac{Net\text{ capitalize cost - residual value}}{term} \\ =\frac{15000-11250}{36}=69.44 \end{gathered}$

Substituting the values into the formula

$\begin{gathered} \text{Finance }\cos t\text{=(14750+11250)}\times0.00271 \\ =26000\times0.00271 \\ =\text{ \ }70.46 \\ \text{Monthly payment=depreciation cost + finance cost} \\ =69.44+70.46=\text{ \ 139.90} \end{gathered}$

The monthly payment should he buys is $418.17 while the monthly payment should he lease is $139.90

Hence, Tim should lease since he would be paying less amount of $139.90