Question

determine the amount needed such that when it comes time for retirement, an individual can make monthly withdraws in the amount of $2,154 for 30 years from an account paying 5.1% compounded monthly. round your answer to the nearest cent.
a. $396,721.78
b. $398,407.85
c. $775,440
d. $1,833,962.40
please select the best answer from the choices provided
a
b
c

Explanation:

Step1: Define variables

Let $P = 2154$ (monthly withdrawal), $r = 0.051$ (annual interest rate), $n = 12$ (compounding periods/year), $t = 30$ (years).

Step2: Calculate monthly rate & total periods

Monthly rate: $i = \frac{r}{n} = \frac{0.051}{12} = 0.00425$
Total periods: $N = n \times t = 12 \times 30 = 360$

Step3: Apply present value formula

Present value of annuity: $PV = P \times \frac{1-(1+i)^{-N}}{i}$
Substitute values:
$PV = 2154 \times \frac{1-(1+0.00425)^{-360}}{0.00425}$
First compute $(1.00425)^{-360} \approx 0.2137$
Then $1 - 0.2137 = 0.7863$
$\frac{0.7863}{0.00425} \approx 185.0118$
$PV \approx 2154 \times 185.0118 \approx 398407.42$

Answer:

b. $398,407.85$