Question

# How much must you deposit at the end of each of the next 14 years so...

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

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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