Question

Find the present value (PV) of the annuity account necessary to fund the withdrawal given. (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $300 per month for 20 years, if the account earns 7% per year and if there is to be $10,000 left in the annuity at the end of the 20 years.

a) $42,981.35
b) $38,500.20
c) $45,672.80
d) $50,000.00

Answer 1

The present value of an annuity is calculated using a formula that considers the regular withdrawals and the final amount remaining. Financial tools or a calculator are needed to compute the complex formula accurately. The total PV is the sum of the PV of monthly withdrawals and the PV of the final amount remaining.

Step-by-step explanation:

To find the present value (PV) of an annuity necessary to fund withdrawals, we need to consider both the regular withdrawals and the final amount left in the annuity. We are given a scenario where $300 is withdrawn per month for 20 years, the account earns 7% per year, and $10,000 must be left in the annuity at the end.

We first calculate the present value of the annuity withdrawals using the formula for the PV of an ordinary annuity:

PV = PMT × [(1 - (1 + r)^-n) / r]

where PMT = $300, r = 7%/12 per month, and n = 20 × 12 months. Then, we calculate the present value of the $10,000 that needs to be left over, which is a single future value, using the formula:

PV of $10,000 = FV / (1 + r)^nLastly, we add both present values to get the total amount needed to be invested today. The correct calculation requires financial tools or a financial calculator to handle the annuity formula complexity.