The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations. If a company wishes to accumulate $500,000 in 20 years at 5% by making equal yearly deposits into an account, calculation of the deposits is an application of the
A) future value of a single amount
B) present value of a single amount
C) future value of an annuity
D) present value of an annuity

Question

Quizplus · Accepted Answer

This problem involves finding the deposits necessary to accumulate a future sum using equal yearly contributions. This is an application of the future value of an annuity formula, which is found in Table 9-4 in the text. The formula is:

FV = PMT x ((1 + r) ^ n - 1) / r

Where FV is the future value, PMT is the equal yearly deposit, r is the interest rate, and n is the number of periods (years in this case).

We are given that FV = $500,000, r = 5%, and n = 20. Plugging in these values and solving for PMT, we get:

$500,000 = PMT x ((1 + 0.05) ^ 20 - 1) / 0.05
$500,000 = PMT x 24.207
PMT = $20,651.54

Therefore, the company must make equal yearly deposits of $20,651.54 to accumulate $500,000 in 20 years at 5%.

The Solution to This Problem Requires Time Value of Money