You would like to have enough money saved to receive a growing annuity for 20 years,growing at a rate of 5% per year,with the first payment of $50,000 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 10%.)
A)$1,000,000.00
B)$425,678.19
C)$605,604.20
D)$827,431.28

Question

Quizplus · Accepted Answer

To calculate the present value of the growing annuity, we can use the formula:

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

where:
PMT = first payment = $50,000
r = interest rate = 10%
g = growth rate = 5%
n = number of payments = 20

Plugging in the values, we get:

PV = ($50,000 / (0.10 - 0.05)) * (1 - (1 + 0.05)^-20)
PV = $605,604.20

Therefore, we would need to save $605,604.20 in our retirement fund to achieve the goal. Option C is the correct answer.

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