A self -employed person deposits $3000 annually in a retirement account (called

Question

A self -employed person deposits $3000 annually in a retirement account (called a Keogh account) that earns 8%.

A.) How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 40?

B.) How much additional money will be in the account if the saver defers retirements until age 70 and continues the contribution?

C.) How much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70?

Please show all work and explain each answer in detail. Thank you so much:-)

Explanation / Answer

a. How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 40?

- FV = PV * PMT

- PV of Annuity = $3,000 x [1-(1.08)-25] / 0.08

PV of Annuity = $32,024.33

FV = $32,024.33 x (1.08)25

FV = $219,318

b. How much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions?

- PV of Annuity = $3,000 x [1-(1.08)-30] / 0.08

PV of Annuity = $33,773.35

FV = $33,773.35 x (1.08)30

FV = $339,849.63

Additional Money = $339,849.63

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