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.

Answer 1

Answer:

The amount needed at the retirement age is $396,721.78.

Step-by-step explanation:

In this problem we need to determine the present value.

Present value is the current value of any future amount that has been invested at a compound interest.

The formula to compute the present value is:

$PV=A\times[\frac{1-(1+\frac{i}{n})^{-t\times n} }{\frac{i}{n} }]$

Here A = Amount withdrawn every month = $2,154

i = rate of interest = 5.1% compounded monthly

t = number of years = 30 years

n = number of withdrawals done each year = 12

Compute the present value as follows:

$PV=A\times[\frac{1-(1+\frac{i}{n})^{-t\times n} }{\frac{i}{n} }]\\=2154\times[\frac{1-(1+\frac{0.051}{12})^{-30\times12} }{\frac{0.051}{12} }]\\=2154\times\frac{0.78276}{0.00425} \\=396721.7789\\\approx396721.78$

Thus, the amount needed at the retirement age is $396,721.78.