An individual is currently 30 years old and she is planning her financial needs

Question

An individual is currently 30 years old and she is planning her financial needs upon retirement. She will retire at age 65 (exactly 35 years from now) and she plans on funding 20 years of retirement with her investments. Ignore any social security payments and ignore any taxes. She made $88,000 last year and she estimates she will need 75% of her current income in today's dollars to live on when she retires. She believes that inflation will average 3 percent per year during her working years. (For simplicity we will ignore inflation during her retirement years). She will retire at age 65 and will begin drawing down her retirement annuity at age 65. She plans on making a total of 20 annual withdrawals after she retires. After she retires she believes she will be able to earn 5 percent per year. If she puts her money in a blended stock and bond portfolio now, she figures she can earn 10.5 percent per year until she retires.

Explanation / Answer

She will need 75% of her current income in today's dollars to live on when she retires

She believes that inflation will average 3 percent per year during her working years

Her current income = $88,000

She will retire at age 65 (exactly 35 years from now)

Therefore money she needs every year after retirement = 75% * $88,000 *(1+3%) ^35

= $185,714.922

She plans on making a total of 20 annual withdrawals of $185,714.922, after she retires. After she retires she believes she will be able to earn 5 percent per year

Therefore Present value of the total of 20 annual withdrawals of $185,714.922 at the time of retirement can be calculated with the help of PV of an Annuity formula

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value at the time of retirement (PV) =?

PMT = Annual payment =$185,714.922

n = N = number of payments = 20 years

i = I/Y = interest rate per year =5%

Therefore,

PV = $185,714.922 * [1- (1+5%) ^-20]/5%

= $2,430,139.34

Now this amount will be future value of her current annual savings for 35 years at the rate of 10.5% annual interest rate

For that we can use FV of an Annuity formula to calculate the annual savings by her

FV = PMT *{(1+i) ^n1} / i

Where,

Loan amount after two years FV =$2,430,139.34

PMT = Annual savings =?

n = N = number of payments = 35 years

i = I/Y = interest rate per year =10.5%

Therefore,

$2,430,139.34 = Annual savings *{(1+10.5%) ^351} / 10.5%

Annual savings = $7,989.71 (Assumed that she is saving at the end of year)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.