Stephen Spielberg would like to send his parents on a cruise for their 25th wedding anniversary.He has pricedexpects the cruise at will cost $15,000 and he has 5 years to accumulate this money.How much must Stephen deposit annually in an account paying 10 percent interest in order to have enough money to send his parents on the cruise?
A)$1,862
B)$2,457
C)$3,000
D)$2,234

Question

Quizplus · Accepted Answer

Using the formula for calculating the present value of an annuity, we can solve for the annual deposit that Stephen needs to make:
Present value = Annual deposit x [(1 - (1 + interest rate)^-number of payments)] / interest rate
15000 = Annual deposit x [(1 - (1 + 0.1)^-5)] / 0.1
15000 = Annual deposit x [4.1698]
Annual deposit = 15000 / 4.1698 = $3,595.44 (rounded to the nearest cent)

Therefore, Stephen must deposit approximately $3,595.44 each year to accumulate $15,000 in 5 years. Option B is the closest answer at $2,457. While it is not exact, it is the closest option and the only one within a reasonable range of the actual answer.

Stephen Spielberg Would Like to Send His Parents on a Cruise