Answer to Question #246798 in Financial Math for Surendra Singh

Question

After retiring, you want to be able to take $1000 every month for a total of 20 years from your retirement account. The account earns 6% interest. How much will you need in your account when you retire?

Answer 1

This question requires us to determine the principal(starting amount, principal). To find its value, the payout annuity formula given below is used.

Payout annuity formula,

$P_0=m(1-(1+r/n)^{-Z*(n)})/(r/n)$ where,

$P_0$ is the balance in the account at the beginning(starting amount , principal)

$m$ is the regular withdrawal

$r$ is the annual interest (decimal form)

$n$ is the number of compounding periods in one year

$Z$ is the number of years we plan to take withdrawals.

From the information above, we are given,

$m=1000$

$r=6\%=0.06$

$n=12$

$Z=20$

Substituting this in the formula,

$P_0=1000*(1-(1+0.06/12)^ {(-20*(12)})/(0.06/12)$

$P_0=1000*(1-(1.005)^{-240})/0.005$

$P_0=1000*(1-0.3020961)/0.005$

$P_0=1000*0.6979039/0.005=697.9039/0.005=139580.80$

Therefore, I will need $139,580.80 in my account when I retire.