Question

A self-employed person deposits $2,000 annually in a retirement account (called a Keogh or H.R. 10 plan) that earns 8 percent. Use Appendix A and Appendix C to answer the questions. Round your answers to the nearest dollar.

1. 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?
   $  

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

3. 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?
   $  

Answer 1

Annual Deposit in Retirement account = $2,000

1). Calculating the vallue in account if individual retire at 65 using Future Value formula:-

where, C = Periodic Depsoit = $2,000

r = periodic Interest rate = 8%

n = no of years = 65 - 40 = 25 years

Future Value = $146,211.88

So, amount in the account when the individual retires at the age of 65 is $ 146,211.88

b). Calculating the vallue in account if individual retire until 70 and continue contribution using Future Value formula:-

where, C = Periodic Depsoit = $2,000

r = periodic Interest rate = 8%

n = no of years = 70 - 40 = 30 years

Future Value = $226,566.42

So, amount in the account when the individual retires at the age of 70 is $ 226,566.42

Additional money will be in the account if the saver defers retirement until age 70 and continues the contributions = Future Value until age 70 - Future Value until age 65

= $226,566.42 - $146,211.88

= $80,354.54

c). Employee discountinue contribution at age 65 but retirre at age 70 which means that after age 65 and until age 70 only Interest will be earned on amount accumulated till age 65

Amount accumulated till age 65 = $146,211.88

Calculating The Future Value at age 70 with only Interest Earned:-

where, Amount = $146,211.88

r = periodic Interest rate = 8%

n = no of years = 5 years

Future Value = $214,833.22

Additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70 = $214,833.22 - $146,211.88

= $68,621.34