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 7% 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 $120,000 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 $550,000 to your children. How much do you have to save each year to make this retirement plan happen?
Solution :
Here, we can calculate,
Required saving per year ( P ) = FVA / [ { ( 1 + r )^n - 1 } / r ]
Then, we have,
Interest per annum = 7%
Number of years = 20
Number of payments per annum = 1
Interest rate per period ( r ) = 7% / 1 = 7%
Number of periods ( n ) = 20 / 1 = 20
Now,
Future value of annuity ( FVA ) = PV(3.5%,30,120000,550000)
FVA = $ 2,402,998.58
Therefore,
Required saving per year ( P ) = 2,402,998.58 / [ { ( 1 + 7% )^20 - 1 } / 7% ]
= $ 58,616.17
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