Stephen would like to send his parents on a cruise for their 25th wedding anniversary. He expects the cruise 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 future value of an annuity:
FV = Pmt x (((1 + r)^n) - 1) / r
Where:
Pmt = Annual payment
r = Interest rate (as a decimal)
n = Number of payment periods

In this case,
FV = $15,000
r = 10% = 0.10
n = 5

Plugging in these variables and solving for Pmt, we get:
$15,000 = Pmt x (((1 + 0.10)^5) - 1) / 0.10
$15,000 = Pmt x 4.868

Therefore, Pmt = $3,082.28 per year

However, we need to adjust this value for compounding. If Stephen makes annual payments, the interest will only compound once a year. Therefore, we can use the formula for future value of a single sum to find the adjusted payment amount:
FV = Pmt x (1 + r)^n

In this case,
FV = $15,000
r = 10% = 0.10
n = 5

Plugging in these variables and solving for Pmt, we get:
$15,000 = Pmt x (1 + 0.10)^5
$15,000 = Pmt x 1.61051

Therefore, Pmt = $9,311.04 / 6 = $2,457.01 per year

Thus, Stephen needs to deposit approximately $2,457 annually in order to accumulate enough money in 5 years to send his parents on the cruise. The answer is closest to option B) $2,457.

Stephen Would Like to Send His Parents on a Cruise