You are 40 years old and want to retire at age 60. Each year, starting one year
ID: 2806996 • Letter: Y
Question
You are 40 years old and want to retire at age 60. Each year, starting one year from now, you will deposit an equal amount into a savings account that pays 6.8% interest. The last deposit will be on your 60th birthday. On your 60th birthday you will switch the accumulated savings into a safer bank account that pays only 3.5% interest. You will withdraw your annual income of $ 130,000 at the end of that year (on your 61st birthday) and each subsequent year until your 90th birthday. On that birthday you want to give$ 700,000 to your children. How much do you have to save each year to make this retirement plan happen?
Explanation / Answer
Find the value of withdrawals at 60th birthday.
PV of annuity = P*[(1-(1+r)^(-n)) / r]
P - Periodic payment = 130000
r - rate per period = 0.035
n - number of periods = 90-60 = 30
PV of annuity = 130000*((1-(1+0.035)^(-30)) / 0.035) = $2390965.90
Value of $700000 = 70000/(1+0.035)^30 = $249394.89
Total value to be saved = 2390965.90 + 249394.89 = $2640360.79
Future value of annuity = $2640360.79
FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = ?
r - rate per period = 0.068
n - number of periods = 60-40 = 20
2640360.79 = P*(((1+0.068)^20 - 1)/0.068)
P = $65825.98
Annual saving = $65825.98
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