Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 32 years and anticipate they will need funding for an additional 23 years. They determined that they would have a retirement income of ​$73,000 in​ today's dollars, but they would actually need ​$104,631 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income​ shortfall, assuming a 3 percent inflation rate and a return of 8 percent.

The total amount that Peter and Blair must save if they wish to completely fund their income​ shortfall, assuming a 3 percent inflation rate and a return of 8 percent is

Answer 1

The amount that Peter and Blair need to save today is $35,781.99

Peter and Blair's income shortfall is $104,631 - $73,000 = $31,631.

This is the income they will need after the first year of their retirement. However, since the inflation rate is 3% this figure will also need to grow by 3% each year so that the Peter and Blair maintain their purchasing power.

We need to find their required income in each year which would be 31,631 in Year 1, 31,631(1.03) in year 2, 31,631(1.03)^2 in year 3 and so on till year 23 (since they will need funding for 23 years).

Then, we need to discount these payments by the rate of return, which is 8% p.a. After that, we will add up the present values of these payments to arrive at the present value which will be after 32 years (this is because Peter and Blair, plan to retire after 32 years. Hence, the first payment would be after that).

This PV at the end of year 32 needs to be discounted further at 8% for 32 years which will give us the value they need to save today so that they can have the above mentioned income during their retirement years.

Below is the calulcation.

Had to upload two screenshots, since, the entire calculation is not fitting in one.

The amount that Peter and Blair need to save today is $35,781.99

Hope this helps.

All the best!!