# Sara Woodyard, age forty-four, plans to retire at age sixty-seven. Her life expectancy, accountin...

Sara Woodyard, age forty-four, plans to retire at age sixty-seven. Her life expectancy, accounting for family medical history, is age ninety-seven. Tara is single and currently earns \$56,000 per year as a university librarian. At her normal retirement age, she expects to receive \$28,700 in Social Security benefits (today’s dollars). She will also receive a small defined benefit pension in the amount of \$13,500 from a local municipality. She has come to you to determine whether she is on track to meet her retirement goal. Use the following assumptions and information to answer the questions that follow:

• She would like to use a 90 percent income replacement ratio, based on current earnings.

• She is currently contributing \$2,400 per year into a 403(b) plan [no employer match].

• Inflation is assumed to be 3.50 percent.

• She can earn a 6.50 percent after-tax rate of return on assets before retirement.

• She can earn a 4.50 percent after-tax rate of return on assets after retirement.

1. How much does Tara need, on her first day of retirement, to fund a capital depletion model

of retirement?

2. Given her current level of savings, is Tara on target to reach her retirement goal?

3. If she has a capital needs shortfall, how much more must she save per year to reach her goal?

4. If she would like to obtain a capital preservation goal for retirement, how much will she need to have saved on her first day of retirement?

5. Given a capital preservation goal, is she saving enough on a yearly basis currently?

6. How much, in total, must she save yearly to reach a capital preservation model of retirement?

Tara's need is =\$50400( 90%*\$56000) Income replacement model.

First Let us ascertain Tara's need on the first day of retirement

If Tara is going to need \$50400 for 30 years , hence the future vale of this total need would be \$26081782.93 by formula

FVAn= A[(1+k)^n-1]/k assuming inflation to be 3.5%

The present Value of this amount would be ( Discounting factor =4.5%) will be \$ 694739.04, hence this would be Tara's need on the first day of retirement.

Now look at the avenue she has on the first day, to find whether she is on target or not

The future value of annuity investment in which she contributes \$ 2400 is \$ 120,235.78 on the retirement day, if we calculate its FV based on 4.5% the value would be \$450282.99 and the annuity it can give on yearly basis based on the above formula will be \$7381.68

Hence the total of retirement benefit at the time of retirement is = \$28700+\$13500+\$7381.68 = \$ 49581.68

Hence there is a shortfall of = \$50400-\$49581.68=\$818.32

She is having a shortfall of \$818.32

Now the question how much doe she need to save till retirement to cover the shortfall.

For this we need to find the PV of Annuity of \$818.32 at the time of retirement,

we will use formula

A= PVAN[k(1+k)^n]/[(1+k)^n-1], the PV comes out as \$13331.08

Now in order to have this amount at the retirement Tara needs to save \$ 266.1 additionally per year this was calculated by using the formula

FVAn= A[(1+k)^n-1]/k

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