You would like to have enough money saved to receive a $64,960 per year after retirement in perpetuity. How much would you need to have saved in your retirement fund to achieve this goal? Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 6 percent. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Question
You would like to have enough money saved to receive a $64,960 per year after retirement in perpetuity. How much would you need to have saved in your retirement fund to achieve this goal? Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 6 percent. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
To calculate the amount you need to save for retirement to receive a certain amount per year in perpetuity, you can use the formula for the present value of a perpetuity. The formula is:
PV = C / r
where:
- PV is the present value, or the amount you need to save,
- C is the cash flow per period, or the amount you want to receive per year, and
- r is the interest rate.
In this case, you want to receive $64,960 per year (C) and the interest rate is 6 percent, or 0.06 (r). Substituting these values into the formula gives:
PV = $64,960 / 0.06
Calculating this gives:
PV = $1,082,666.67
So, you would need to have saved approximately 64,960 per year in perpetuity.
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