Question

​(Compounding using a calculator​) Bart​ Simpson, age 9​, wants to be able to buy a really cool new car when he turns 18. His really cool car costs ​$15 comma 000 ​today, and its cost is expected to increase 2 percent annually. Bart wants to make one deposit today​ (he can sell his​ mint-condition original Nuclear Boy comic​ book) into an account paying 7.2 percent annually in order to buy his car in 9 years. How much will​ Bart's car​ cost, and how much does Bart have to save today in order to buy this car at age 18​?

Answer 1

Price of the car now P = $15000

Car price increases by i = 2% each year

Price of the car after n years = P(1+i)ⁿ = 15000(1+0.02)⁹ = $17926.38

Let the amount deposited by Bart be X

Interest rate on the deposit = r = 7.2%

Value of the deposit after 9 years = X(1+0.072)⁹

The value of deposit in 9 years should be equal to the value of the car in 9 years for Bart to purchase it

Hence, X*1.072⁹ = 17926.38

=> X = $9588.25

Hence, Bart should deposit $9588.25 now to buy the car in 9 years