Question

# You are 40 years old and want to retire at age 60. Each​ year, starting one...

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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