You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement.How much would you need to save in your retirement fund to achieve this goal? The interest rate is 12 percent.
A)$1,500,000
B)$632,390
C)$452,165
D)$1,043,287

Question

Quizplus · Accepted Answer

This question requires us to use the present value of a growing annuity formula. We know that the annuity will last for 25 years, with the first payment occurring in one year. The annuity is growing at 4 percent per year, and the interest rate is 12 percent.

Using the formula:

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

where PV is the present value, C is the first payment, r is the interest rate, g is the growth rate, n is the number of years,

We can plug in the values:

PV = 60,000 / (0.12 - 0.04) * (1 - ((1 + 0.04) / (1 + 0.12))^25)

PV = $632,389.85

Therefore, we would need to save $632,390 in our retirement fund to achieve our goal. The best answer is B.

You Would Like to Have Enough Money Saved to Receive