You are now 30 years old. You plan to retire in 30 years, and expect to live for 30 years after retirement, that is, until you are 90. You want a fixed retirement income that has the same purchasing power at the time you retire as $80,000 has today. You realize that the real value of your retirement income will decline year-by-year after you retire. Your retirement income will begin the day you retire, 30 years from today, and you will then get 29 additional annual payments. Inflation is expected to be 5% per year from today forward. You currently have $250,000 in your savings account earning 7% per year, annual compounding. How much must you save during each of the next 30 years (with deposits being made at the end of each year) to meet your retirement goal?
To determine how much you need to save during each of the next 30 years, you need to calculate the present value of your retirement goal using the concept of inflation and discounting.
Step 1: Calculate the future value of $80,000, adjusted for inflation.
Since you expect inflation to be 5% per year, you need to calculate the future value of $80,000 over a 30-year period. The formula to calculate the future value is:
Future Value = Present Value * (1 + Inflation Rate)^Number of Years
Plugging in the values:
Future Value = $80,000 * (1 + 0.05)^30
Future Value = $80,000 * 1.05^30
Future Value ≈ $217,369.42
Therefore, you need a retirement income of approximately $217,369.42 in today's dollars when you retire.
Step 2: Calculate the amount you need to save each year.
To calculate the annual savings required, you need to determine the present value of the future retirement income. The present value formula is:
Present Value = Future Value / (1 + Interest Rate)^Number of Years
You currently have $250,000, which is your starting point. So, the amount you need to save each year is:
Annual Savings = (Present Value - Starting Amount) / Present Value Interest Factor
Using the formula:
Annual Savings = ($217,369.42 - $250,000) / (Present Value Interest Factor)
The Present Value Interest Factor (PVIF) can be calculated based on the interest rate and the number of years. In this case, the interest rate is 7%, so the PVIF can be calculated as:
PVIF = 1 / (1 + Interest Rate)^Number of Years
PVIF = 1 / (1 + 0.07)^30
PVIF ≈ 0.123
Now, plug in the values to calculate the annual savings required:
Annual Savings = ($217,369.42 - $250,000) / 0.123
Annual Savings ≈ $2791.86
Therefore, you would need to save approximately $2,791.86 each year for the next 30 years to meet your retirement goal.