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
[tex]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[/tex]
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:
[tex]C'=C*(1+i)=581,773.42*(1+0.15)=669,039.44[/tex]
