Please review the following case and use it as the basis for your analysis for this unit. Pay careful attention to the situation and note the specific events as they might apply to the information from your chapter. You will use this data to form the basis of your analysis. The specific architecture of your submission may be found in the course Syllabus on page x.
George Thriftless is 45 years old, earns $50,000 per year, and expects that his future earnings will keep pace with inflation, but will not exceed inflation. He has not yet saved anything toward his retirement. His company does not offer any pension plan. George pays Social Security taxes equal to 7.5% of his salary, and he assumes that when he retires at age 65, he will receive $ 12,000 per year in inflation-adjusted Social Security benefits for the rest of his life. His life expectancy is age 85.
George buys a book on retirement planning that recommends saving enough so that when private savings and Social Security are combined, he can replace 80% of his preretirement salary. George buys a financial calculator and goes through the following calculations:
First, he computes the amount he will need to receive in each year of retirement to replace 80% of his salary: 0.8 X $50,000 = $40,000.
Since he expects to receive $12,000 per year in Social Security benefits, he calculates that he will have to provide the other $28,000 per year from his own retirement fund.
Using the 8% interest rate on long-term default-free bonds, George computes the amount he will need to have at age 65 as $274,908 (the present value of $28,000 for 20 years at 8% per year). Then he computes the amount he will have to save in each of the next 20 years to reach that future accumulation as $6,007 (the annual payment that will produce a future value of $274,908 at an interest rate of 8% per year). George feels pretty confident that he can save 12% of his salary (i.e., $6,007/$50,000) in order to ensure a comfortable retirement.
Questions:
* If the expected long-term real interest rate is 3% per year, approximately what is the long-term expected rate of inflation?
* Has George correctly taken account of inflation in his calculations? If not, how
would you correct him?
* How much should George save in each of the next 20 years (until age 65) if he wants to maintain a constant level of consumption over the remaining 40 years of his life (from age 45 to age 85)? Ignore income taxes.
To answer the questions, let's break down the information provided and go step by step.
1. If the expected long-term real interest rate is 3% per year, approximately what is the long-term expected rate of inflation?
To calculate the long-term expected rate of inflation, we subtract the real interest rate from the nominal interest rate. In this case, the nominal interest rate is given as 8%, and the real interest rate is given as 3%. So the long-term expected rate of inflation would be approximately 5% per year (8% - 3%).
2. Has George correctly taken account of inflation in his calculations? If not, how would you correct him?
No, George has not correctly taken account of inflation in his calculations. He assumed that his future earnings will keep pace with inflation, but his savings and retirement calculations do not consider the effects of inflation. To correct this, he would need to adjust his future savings and retirement fund requirements to account for inflation.
Inflation reduces the purchasing power of money over time, so the $40,000 he calculated as the amount he would need to receive in each year of retirement to replace 80% of his salary will not be sufficient due to inflation. He needs to adjust this amount based on the expected rate of inflation. The inflation-adjusted amount can be calculated as the desired amount divided by (1 + inflation rate)^number of years.
In this case, if we assume the long-term expected rate of inflation is 5% per year, George would need to adjust his retirement income requirement as follows:
$40,000 / (1 + 0.05)^20 = $17,242.17 per year.
So he would need to replace $17,242.17 per year in retirement to maintain the same purchasing power that $40,000 has today.
3. How much should George save in each of the next 20 years (until age 65) if he wants to maintain a constant level of consumption over the remaining 40 years of his life (from age 45 to age 85)? Ignore income taxes.
To calculate the amount George should save each year, we need to account for inflation and the time value of money.
First, we calculate the future value of the desired constant level of consumption over the remaining 40 years of his life. Using the real interest rate of 3%, we can compute the future value of $17,242.17 for 40 years at 3% per year:
Future Value = $17,242.17 * (1 + 0.03)^40 = $54,661.49.
Now, we need to calculate the savings required each year to accumulate this future amount. Using the same real interest rate of 3% and the annuity formula, we can compute the annual savings:
Annual Savings = $54,661.49 * [1 - (1 + 0.03)^-20] / 0.03 = $5885.35.
Therefore, George should save approximately $5,885.35 each year for the next 20 years to maintain a constant level of consumption over the remaining 40 years of his life.
Remember, these calculations are simplified and do not account for factors like investment returns, changes in income, or unexpected expenses. It's always important to reassess and adjust saving goals regularly based on changing circumstances.