Question

Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has priced the cruise at $15,000 and she has 5 years to accumulate this money. How much must Janice deposit annually in an account paying 10 percent interest in order to have enough money to send her parents on the cruise?

A)

$3,000

B)

$2,457

C)

$1,862

D)

$2,234

Answer 1

Janice must annually deposit approximately $2,234 in an account with a 10% interest rate to accumulate $15,000 in five years. This is calculated using the future value of an annuity formula, adjusted to solve for the annual payment (Pmt). The choice D) $2,234 from the given options is correct.

Step-by-step explanation:

Janice would like to calculate how much she must deposit annually at a 10 percent interest rate to have $15,000 in five years to send her parents on a cruise.

To solve this, we use the formula for the future value of an annuity:
FV = Pmt * (((1 + r)^n - 1) / r)
where:
FV is the future value of the annuity, which is $15,000,
Pmt is the annual payment,
r is the annual interest rate, which is 0.10,
n is the number of years, which is 5.

We rearrange this formula to solve for Pmt:
Pmt = FV / (((1 + r)^n - 1) / r)

Plugging in the values gives us the annual deposit amount:

Pmt = $15,000 / ((((1 + 0.10)^5 - 1) / 0.10)
Pmt ≈ $2,234

Therefore, the correct answer is D) $2,234.