A cash-strapped young professional offers to buy your car with four, equal end of year annual payments of $3,000, beginning 2 years from today (the first payment will be made on the last day of year 2).Assuming you're indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept?

Question

Quizplus · Accepted Answer

The present value (PV) of the payments can be calculated using the formula for the present value of an annuity due to the payments being made at the end of each period. Since the payments start 2 years from today, and the interest rate is 10%, the calculation is as follows:$$ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)^{-1} $$Where:- $ P = \$3,000 $ (the annual payment),- $ r = 0.10 $ (the annual interest rate),- $ n = 4 $ (the number of payments),- The last part $(1 + r)^{-1}$ adjusts the formula for the fact that the first payment is not received immediately but one period later than a standard annuity due.$$ PV = \$3,000 \times \left( \frac{1 - (1 + 0.10)^{-4}}{0.10} \right) \times (1 + 0.10)^{-1} $$$$ PV = \$3,000 \times \left( \frac{1 - (1 + 0.10)^{-4}}{0.10} \right) \times (1 + 0.10)^{-1} $$$$ PV = \$3,000 \times 3.169865 \times 0.9090909 $$$$ PV = \$8,645.09 $$Since the present value of the payments ($8,645.09) is less than the $9,000 you want for the car, you should not accept the offer.

A Cash-Strapped Young Professional Offers to Buy Your Car with Four