Question

g You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $90,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 15% annually. What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations. $ Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.

Answer 1

Answer:

(a) The amount you need in your retirement account the day yo retire is $581,773.42.

(b) If you take the first withdrawal the day you retire, the amount needed is $669,039.44.

Explanation:

This problem is a case of annuity (n = 25 years).

They plan to withdraw $ 90,000 annually from the end of the first year of retirement.

The formula that relates capital in the account to annual withdrawals is

$C=A*D=A*\frac{(1+i)^{n}-1}{i*(1+i)^{n}} \\\\C=90,000*\frac{(1+0.15)^{25}-1}{0.15*(1+0.15)^{25}}=90,000*6.46414908527014\\\\C= 581,773.42$

If your first withdrawal will be made the day you retire, you can calculate the amount of money in your account as the amount calculated before ($581,773.42) and multiplying it by (1+i)=1.15.

This is because all withdrawals are being advanced in one year, so the current value would be C '= C * (1 + i). Then we have:

$C'=C*(1+i)=581,773.42*(1+0.15)=669,039.44$