Question

Question 4 (1 point) Stephen plans to purchase a car 2 years from now. The car will cost $66,054 at that time. Assume that Stephen can earn 7.35 percent (compounded monthly) on his money. How much should he set aside today for the purchase? Round the answer to two decimal places. Your Answer: Answer Page 4 of 6 Next Page Submit Quiz 3 of 6 questions saved

Answer 1

The amount that is required to be paid in future is known as future value of the money which in this case is $66,054. This amount can be gathered by compounding a specific sum on a monthly basis for 2 years at the rate of 7.35%, the calculation of that particular sum is called calculation of present value. It can be calculated as follows:

PV = FV * (1 /1 +r)ⁿ

Here,

FV = $66,054

r = interest rate in decimal

n = period in months

by applying the formula, we can get the following equation:

7.35 / 100 = 0.0735 , 0.0735 /12 = 0.006125

PV = $66,054 * (1 / 1+ 0.006125)²⁴

        = $66,054 * 1 / 1.1578

       = $66,054 / 1.1578

      = $57,051.30

Hence, Stephen would need $57,051.30 today which can become $66,054 after 2 years, if compounded at the rate of 7.35% on a monthly basis.