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Consider the following two options for financing a car:
Option A. Purchase the vehicle at the normal price of \$26,200 and pay for the vehicle over three years with equal monthly payments at 1.9% APR financing.
Option B.Purchase the vehicle for a discount price of \$24,048, to be paid immediately.
The funds that would be used to purchase the vehicle are presently earning 5% annual interest compounded monthly.
(a) What is the meaning of the APR of 1.9% quoted by the dealer?
(b) Under what circumstances would you prefer to go with the dealers financing?
(c) Which interest rate (the dealers interest rate or the savings rate) would you use in comparing the two options?
In calculating the net cost of financing the car, we need to decide which interest rate to use in discounting the loan repayment series. Note that the 1.9% APR represents the dealer’s interest rate to calculate the loan payments. With the 1.9% interest, your monthly payments will be A = \$26,200(A/P, 1.9%/12,36) =\$749.29. On the other hand, the 5% APR represents your earning opportunity rate. In other words, if you do not buy the car, your money continues to earn 5%APR. Therefore, this 5% rate represents your opportunity cost of purchasing the car. Which interest rate should we use in this analysis? Since we wish to calculate each option’s present worth to you. given your money and financial situation, we must use your5 % interest rate to value these cash flows. Given:The loan paymenl series shown in Figure 3.12,r = 5%, payment period=monthly, and compounding period= monthlly We have to find the…

ost economical financing option. For each option, we will calculate the net equivalent cost (present worth) at n =0. Since the loan payments occur monthly, we need to determine the effective interest rate per month, which is 5%/12. Option A (conventional financing): The equivalent present cost of the total loan repayments is calculated as PA = \$749.29(P/A, 5%/12,36) = \$25,000. Option B (cash payment): Since the cash payment is a lump sum to be paid presently, its equivalent present cost is equal to its value: PB = \$24,048. Thus, there would be \$952 of savings in present value with the cash payment option.

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