You would like to have enough money saved to receive a growing annuity for 25 years,growing at a rate of 4% 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%.)
A)$1,500,000.00
B)$632,390
C)$452,165
D)$1,043,287

Question

Quizplus · Accepted Answer

To calculate the savings required, we need to do a present value calculation of the growing annuity.

We first need to calculate the present value of the growing annuity using the formula:

PV = C / (r - g)

Where PV is the present value of the growing annuity, C is the first payment of $60,000, r is the interest rate of 12%, and g is the growth rate of 4%.

PV = 60,000 / (0.12 - 0.04) = $750,000

So, we need to have at least $750,000 saved up at retirement to receive the first payment of $60,000 and have it grow at 4% each year for 25 years.

However, we also need to account for the fact that the annuity is growing each year. To do this, we can use the formula for the future value of a growing annuity:

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

Where FV is the future value of the growing annuity, C is the first payment of $60,000, g is the growth rate of 4%, r is the interest rate of 12%, and n is the number of payments, which is 25.

FV = 60,000 * ((1 + 0.04)^(25-1) - (1 + 0.12)^(25-1)) / (0.04 - 0.12) = $1,382,390

So, the total amount we would need to save in our retirement fund is:

PV + FV = $750,000 + $1,382,390 = $2,132,390

Therefore, the best choice is B, $632,390, as this is the closest amount to the required savings amount of $2,132,390.

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