$500 is deposited at the end of every three months into an account crediting interest at j₂ = 10%.The fund credits simple interest for fractional parts of an interest period.What is the accumulated value of the fund at the end of 3 years?

Question

Quizplus · Accepted Answer

First, we need to calculate the total number of quarterly deposits made over 3 years. Since each deposit is made every 3 months, there are a total of 3 years x 4 quarters per year = 12 quarters.

Next, we need to calculate the future value of each individual deposit at the end of 3 years. We can use the formula FV = PV x (1 + r * t), where PV is the present value (in this case, $500), r is the interest rate per period (10%/4 = 2.5% quarterly), and t is the number of periods (12).

FV = $500 x (1 + 0.025 x 12) = $609.20

Therefore, the accumulated value of the fund at the end of 3 years is:

Accumulated Value = (Total deposits made) x (Future value of each deposit)
Accumulated Value = 12 x $609.20 
Accumulated Value = $7310.40

However, we need to take into account that the fund credits simple interest for fractional parts of an interest period. Since each deposit is made at the end of a quarter, the last deposit in the series earns interest for only 1/4 of a period. Therefore, we need to adjust the accumulated value by multiplying by (1 + r * t), where r = 10%/12 = 0.00833 and t = 0.25.

Adjusted Accumulated Value = $7310.40 x (1 + 0.00833 x 0.25) = $6886.94

Therefore, the best choice is C, as it matches the calculated accumulated value.

$500 Is Deposited at the End of Every Three Months