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.
The future value of equal semi-annual payments of $500 at 8% compounded semiannually for 4 years is
A) $868
B) $2,000
C) $4,607
D) $9,320

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. ​
The future value of equal semi-annual payments of $500 at 8% compounded semiannually for 4 years is
A) $868
B) $2,000
C) $4,607
D) $9,320

Quizplus · Accepted Answer

Using Table 9-2 in the text, the semi-annual interest rate is 4% (8%/2) and the number of semi-annual periods is 8 (4 years x 2 semi-annual periods per year).

Using Table 9-4, the future value factor for an 8-period annuity at a 4% semi-annual interest rate is 9.2144.

Multiplying the annual payment of $500 by 2 for semi-annual payments gives a semi-annual payment of $1,000.

The future value of the 8 semi-annual payments of $1,000 is:

$1,000 x 9.2144 = $9,214.40

However, this is the future value of all 8 semi-annual payments. To find the future value of equal semi-annual payments of $500, we need to divide this amount by 2:

$9,214.40 ÷ 2 = $4,607.20

Therefore, the future value of equal semi-annual payments of $500 at 8% compounded semiannually for 4 years is $4,607. Answer choice C is the correct answer.

The Solution to This Problem Requires Time Value of Money