You would like to have enough money saved to receive a $65,326 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 8 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 $65,326 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 8 percent. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
Alright, let's break this down.
You want to have enough money saved so that you can receive $65,326 per year forever after you retire. To figure out how much you need to save, we need to calculate the present value of this perpetuity.
Here's how we do it:
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We start with the formula for the present value of a perpetuity: PV = D / r, where D is the annual payment and r is the interest rate.
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In this case, D is $65,326 and r is 8% or 0.08 in decimal form.
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So, we plug these values into the formula: PV = 816,575
So, you would need to have 65,326 per year forever after retirement, assuming an annual interest rate of 8%. This means that, considering the future payments you'll receive and the interest rate, you need to save about $816,575.00 before you retire.
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