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 $106,000 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 5.5 percent per year. If she puts her money in a blended stock and bond portfolio now, she figures she can earn 11 percent per year until she retires.

Questions:

1. How much money will she need to withdraw each year starting at age 65 to have the same purchasing power as today? I got $223702.07 for this answer. I am struggling with the following two questions.

2. How much money must she have at age 65 in order to make her planned withdrawals?

3. How much should she save per year starting right now in order to have the retirement annuity she desires?

Answer 1

Answer 1:

Given:

• She will retire at age 65 (exactly 35 years from now)
• She made $106,000 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.

Hence:

Money will she need to withdraw each year starting at age 65 = 106000 * 75% * (1 + 3%) ³⁵ = $223702.0651

Money will she need to withdraw each year starting at age 65 = $223,702.07

Answer 2:

We calculated above:

Money will she need to withdraw each year starting at age 65 = $223,702.07

Given:

• After retirement she plans on funding 20 years of retirement with her investments.
• 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
• After she retires she believes she will be able to earn 5.5 percent per year.

Hence:

It is an annuity due.

PMT = $223,702.0651

N = 20

I/Y = 5.5%

Hence:

Money must she have at age 65 = PV (rate, nper, pmt, fv, type) = PV (5.5%, 20, -223702.0651, 0, 1)

= $2,820,358.13

Money must she have at age 65 = $2,820,358.13

Answer 3:

We calculated above:

Money must she have at age 65 = $2,820,358.13

Given:

• She wants to save starting right now every year
• If she puts her money in a blended stock and bond portfolio now, she figures she can earn 11 percent per year until she retires.

Hence:

It is an annuity due

FV = $2,820,358.13

PV =0

N = 35

I/Y = 11%

Hence

Amount she should save per year starting right now = PMT (rate, nper, pv, fv, type)

= PMT (11%, 35, 0, -2820358.13, 1)

= $7,438.35

Amount she should save per year starting right now = $7,438.35