Starting in 5 years and 6 months you want to be able to withdraw $950 every three months for 3 years and 3 months. You want to deposit a single amount immediately and then let it grow at a rate of 7.24% compounded quarterly. How much interest did you earn during the entire period of time?

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the withdrawals. Using the formula for the present value of an annuity, we get:

PV = C * (1 - (1+r)^-n) / r

where PV is the present value, C is the periodic payment, r is the interest rate per period, and n is the total number of periods.

Here, C = $950, r = 0.0724/4 = 0.0181 (quarterly rate), and n = 3*4 + 3 = 15 (15 quarterly payments). Plugging in these values, we get:

PV = 950 * (1 - (1+0.0181)^-15) / 0.0181 = $12,280.08

This means that you need to deposit $12,280.08 today to be able to withdraw $950 every three months for 3 years and 3 months, starting in 5 years and 6 months.

Next, we need to calculate the future value of this deposit after the entire period of time. Using the formula for compound interest, we get:

FV = PV * (1 + r)^n

where FV is the future value, PV is the present value, r is the interest rate per period, and n is the total number of periods.

Here, PV = $12,280.08, r = 0.0724/4 = 0.0181 (quarterly rate), and n = 5*4 + 6 + 3*4 + 3 = 35 (35 quarterly periods). Plugging in these values, we get:

FV = 12,280.08 * (1 + 0.0181)^35 = $21,139.55

Finally, we need to subtract the initial deposit from the final value to get the interest earned:

Interest = FV - PV = 21,139.55 - 12,280.08 = $8,859.47

Therefore, the answer is D) $4859.47 (rounded to the nearest cent).

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