Question

Eleanor needs $40,000 a year to live on in retirement net of the income she will receive. She will be retiring in 22 years and is funding for a 25-year retirement. The inflation rate is expected to be 3.5 percent a year and the after-tax return on her investments 6 percent.

a) How much will she fall short to at the beginning of the retirement period?

b) What lump sum will she need at the beginning of the retirement period?

c) What is the required yearly savings?

Answer 1

Solution a) Eleanor currently needs $40,000 per year.

The expenses will grow at inflation rate of 3.5%.

Time period = 22years

N = 22;

PMT = 0;

I/Y 3.5%;

PV = -40,000;

CPT → FV = 85,260

She fall short by $85260 at the beginning of the retirement period

Solution b)We need to calculate real rate of return before we can calculate lump sum amount.

Real rate of return= ((1+investment rate of return)/(1+inflation rate)-1)

= 2.42%

No. of years = 25

PMT = $(85,260.46)

I/y = 2.42%

FV = 0

PV = $1,586,168.62

Lump sum required = $1586168.62

Solution c) No. of years = 22

I/y = 6.00%

As we have estimated future cashflow requirement after taken effect of Inflation so now we only take investment return not real rate of return.

FV = $1,586,168.62

PV = 0

PMT = $(36,554.16)

Yearly saving will be = $36554.16

Note: I used the BA II Plus calculator for solving this questions, Please feel free to reach me if further clarification is required with any questions.