Question

Your goal is to be able to withdraw $5,100 for each of the next six years beginning one year from today. The return on the investment is expected to be 11%. The amount that needs to be invested today is closest to: (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided.)

a. $21,576.
b. $29,616.
c. $37,970.
d. $30,600.

Answer 1

The closest amount that needs to be invested today to be able to withdraw $5,100 for each of the next six years at an 11% interest rate, using the present value of an annuity (PVA) calculation, is approximately $29,616.

Step-by-step explanation:

To determine the present value of withdrawals totaling $5,100 per year for six years at an interest rate of 11%, we need to use the present value of an annuity (PVA) formula:
PV = PMT * [((1 - (1 + r)^{-n}) / r)],

where PV is the present value, PMT is the periodic payment, r is the periodic interest rate, and n is the total number of payments.

For this scenario:
PMT = $5,100
r = 0.11
n = 6

Using a financial calculator or PVA table with these values:

PV = $5,100 * ((1 - (1 + 0.11)^{-6}) / 0.11)
= $5,100 * 4.1114
= $20,978.34 (approximate value using a PVA factor).

Hence, the closest amount that needs to be invested today is b. $29,616.