Question

ne that you plan to retire 40 years from now and ou expect to need $2M to support the lifestyle Assume that you plan that you expect to nee that you want. If the interest rate is 10%, is the following state- ment approximately true? “Waiting 5 start saving doubles what you must deposit each s to year." (b) If the interest rate is 12%, is the required multi- plier higher or lower than for the 10% rate in (a)? (c) At what interest rate is the following statement exactly true? “Waiting 5 years to start saving doubles what you must deposit each year.”

Answer 1

a)

If you plan to retire in 40 years, the annual deposit to be made to reach the retirement goal of $ 2 million is calculated as follows.

Al (1+r)-1] Future value annuity =

$2,000,000 = A[(1 + 0.10) 40 - 1] 0.10

A = $ 4,518.83

Waiting for 5 years to start the savings, the annual deposit to be made is calculated as below

$2,000,000 = A[(1 + 0.10) 35 – 1] 0.10

A = $7,379.41

If 5 years is waited to start the savings, the required multiplier is

$7,379.41 Multiplier = S 4.518.83

Multiplier = 1.63

Hence it is not true that waiting for 5 years to start the savings doubles what must be deposited each year.

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b)

If the interest rate is 12%, the annual deposit to be made to reach the retirement goal of $ 2 million is calculated as follows.

$2,000,000 = A[(1 +0.12) 40 - 1] 0.12

Annual deposit = $2,607.25

Waiting for 5 years to start the savings, the annual deposit to be made is calculated as below

$2,000,000 = A[(1 + 0.12) 35 - 1] 0.12

Annual deposit = $4,633.24

If 5 years is waited to start the savings, the required multiplier is

Multiplier = $4633.24 $267.25

Multiplier = 1.78

At a rate of 12%, the required multiplier is higher than for the 10% rate.

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c)

Thus at an interest rate of 12%, the following statement is approximately true that " waiting 5 years to start saving doubles what you must deposit each year".