Question

How much must you deposit at the end of each of the next 14 years so that beginning fifteen years from now, you can withdraw $10,000 a year for the next six years (periods 15 through 20)? Assume an interest rate of 6% compounded annually.

a.           $2,112.62

b.           $3,512.37

c.           $2,855.09

d.           $2,339.90

e.           $3,333.33

Answer 1

The amount is computed as follows:

Present value of $ 10,000 a year in year 14 will be as follows:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 10,000 x [ (1 - 1 / (1 + 0.06)⁶ ) / 0.06 ]

= $ 10,000 x 4.917324326

= $ 49,173.24326

Now the above value will become the future value as follows:

Future value = Annual amount x [ [ (1 + r)ⁿ – 1 ] / r ]

$ 49,173.24326 = Annual amount x [ [ (1 + 0.06)¹⁴ - 1 ] / 0.06 ]

$ 49,173.24326 = Annual amount x 21.01506593

Annual amount = $ 49,173.24326 / 21.01506593

Annual amount = $ 2,339.90

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