Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,500 deposits at the end of each of the next 15 years. If the annual interest rate is 7.2%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent.

Question

Quizplus · Accepted Answer

To start, we need to calculate how much the $2,500 deposits at the end of each of the next 15 years will grow to in 30 years. We can use the formula for future value of an annuity to find this amount:

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

where PMT is the deposit amount, r is the interest rate, and n is the number of periods. Plugging in the values from the problem, we get:

FV = $2,500 x (((1 + 0.072)^15 - 1) / 0.072) = $73,316.66

Next, we need to calculate how much Bob will have after leaving the money in the account for 5 additional years. To do this, we can use the formula for future value of a lump sum:

FV = PV x (1 + r)^n

where PV is the present value (which in this case is the amount we just calculated, $73,316.66), r is the interest rate, and n is the number of periods. Plugging in the values from the problem, we get:

FV = $73,316.66 x (1 + 0.072)^5 = $90,320.64

Therefore, the answer is A, $90,320.64.

Suppose That Bob Delays Starting an IRA for the First