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 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?

Answer #1

**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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