Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 35 years and anticipate they will need funding for an additional 26 years. They determined that they would have a retirement income of ​$64 comma 000 in​ today's dollars, but they would actually need ​$88 comma 241 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 4 percent inflation rate and a return of 9 percent.

Answer 1

Peter and Blair need to save 4,105.10 USD per year for 35 years until retirement.

Step-by-step explanation:

Peter and Blair actually need 88,241 USD in retirement income to meet all of their objectives.

Current amount they have = 64,000 USD

Time period of Retirement = 35 years

Additional Years = 26 years

Inflation rate = 4%

Rate of return = 9%

So, we have all of that data to solve the problem. Then let's do it.

Our first step is to calculate the real rate of return by incorporating the inflation rate into it. Note: we have been given rate of return not the real rate of return.

Real Rate of Return = ( 1 + ROR given)/(1+ inflation rate) - 1

Real Rate of Return = ( 1+ 0.09)/(1 + 0.04) -1

Real Rate of Return = 0.048 x 100 = 4.80%

So, the real rate of retunr is = 4.80%

Now, let's find out the what is the additional fund required in total:

Additional funds required = Required - Available

Additional funds required = 88,241 - 64,000

Additional funds required = 24,241 USD

Now, we have to calculate the Present value of this additional funds required for the time period of 26 years.

Present value can be calculated by using the finance calculator online.

You have to put these data into the calculator to calculate the present value of the money.

PMT = 24241

Interest Rate (I/Y) = 4.80

Number of Periods (N) = 26 years

By plugging in these numbers, you will the present value of 24,241 USD:

Present Value = 355,770.28 USD

Now, we have to calculate the amount of money Peter and Blair need to save every year till their retirement after 35 years.

For that, I have used that finance calculator this time solving for PMT.

You need to put following data into the calculator:

Future Value = 355,770.28

Number of periods(N) = 35 years

Interest Rate (I/Y) = 4.80%

Annual Payment (PMT) = 4105.10 USD

It means Peter and Blair need to save 4,105.10 USD per year for 35 years until retirement.