Question

Jasmine Amberlin, age 40, single, and from Victorville, California, is trying to estimate the amount she needs to save annually to meet her retirement needs. Jasmne currently earns $30,000 per year. She expects to need 80 percent of her current salary to live on at retirement. Jasmine anticipates that she will receive $800 per month in Social Security benefits. Assume Jessica will be retired for 25 years and that she earns 3% beyond inflation and taxes in her retirement investments.

(a) What annual income would Jasmine need for retirement?

(b) What would her annual expected Social Security benefit be?

(c) Jasmine expects to receive $500 per month from her defined-benefit pension at work. What is her annual benefit?

(d) How much annual retirement income will she need from her retirement funds?

(e) How much will Jasmne need to save by retirement in today’s dollars if she plans to retire at age 65 and live to age 90?

(f) Jasmine currently has $5000 in a traditional IRA. Assuming a growth rate of 8 percent, what will be the value of her IRA when she retires?

(g) How much additional money will she still need to save for retirement?

(h) What is the amount she needs to save each year to reach this goal?

Answer 1

Part a)

Annual income after retirement = Current salary $30,000 * 80% i.e. $24,000 / year

Part b)

Annual expected Social Security benefit = Social security benefits $800 / month * 12 i.e. $9,600 / year

Part c)

Annual defined benefit pension work = Monthly receipt $500 * 12 i.e. $6,000 / year

Part d)

Annual contribution from retirement funds = Annual income after retirement $24,000 - Social security benefit $9,600 - Annual defined benefit pension work $6,000

Annual contribution from retirement funds = $8,400 / year

Part e)

Total retirement funds required = Annual contribution $8400 * Number of years post retirment 25 (90-65)

Total retirement funds required = $210,000

Return on investment = 3%

Number of years to retirment = 25 (65-40)

Current Value of retirement savings = Total retirement funds required $210,000 / (1+Return on investment 3%)^{Years to retirement 25}

Current Value of retirement savings = $100,297.2

Part f)

Amount in IRA = $ 5000

Growth Rate = 8%

Value on retirement = Current amount $5,000 * (1+Growth rate 8%)^{Number of years to retirement 25}

Value on retirement = $34,242.38

Part h)

Retirment corpus = Total retirement funds required $210,000 - IRA value on retirement $34,242.38 i.e. $175,757.6

Yearly savings can be calculated using future value of annuity equation:

Future Value of Annuity $175,757.6 = Yearly savings * {(1+Rate of return 3%)^{Number of years 25} - 1}/Rate of return 3%

Yearly Savings = $4,820.657