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 Vito has $5,000 per year to invest for 10 years and wants to accumulate $87,745 at the end of that time, he must find an investment that is earning at a rate of
A) 15%
B) 12%
C) 11%
D) 6%

Question

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 Vito has $5,000 per year to invest for 10 years and wants to accumulate $87,745 at the end of that time, he must find an investment that is earning at a rate of
A) 15%
B) 12%
C) 11%
D) 6%

Quizplus · Accepted Answer

Using Table 9-4 (future value of an annuity due of $1) and assuming annual compounding, we can calculate the annual payment Vito needs to make to accumulate $87,745 in 10 years:

$87,745 = Payment x Future Value Annuity Due Factor, n=10, i=rate
$87,745 = Payment x 15.937
Payment = $5,500

Therefore, Vito needs to invest $5,500 per year for 10 years to accumulate $87,745 at the end of that time.

Using Table 9-1 (future value of $1) and assuming annual compounding, we can calculate the rate of return (i) required for Vito to accumulate $87,745 with an annual investment of $5,000 over 10 years:

$87,745 = $5,000 x Future Value Factor, n=10, i=rate
$87,745 = $5,000 x 17.549
17.549 = (1+i)^10
i = 0.1176 or 11.76%

Therefore, Vito needs to find an investment that is earning at least 11.76% per year to accumulate $87,745 at the end of 10 years with an annual investment of $5,000.

The closest answer choice to 11.76% is B) 12%. Therefore, the best choice(s) is B) 12%.

The Solution to This Problem Requires Time Value of Money