SOLUTION: You want to be able to withdraw $40,000 each year for 25 years. Your account earns 8% interest. How much do you need in your account at the beginning?

Algebra ->  Finance -> SOLUTION: You want to be able to withdraw $40,000 each year for 25 years. Your account earns 8% interest. How much do you need in your account at the beginning?       Log On


   

Question 1209857: You want to be able to withdraw $40,000 each year for 25 years. Your account earns 8% interest. How much do you need in your account at the beginning?
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
To determine how much you need in your account at the beginning, we need to calculate the present value of an annuity. Here's how:
**Formula:**
PV = PMT * [1 - (1 + r)^-n] / r
Where:
* PV = Present Value (the initial amount needed)
* PMT = Annual Payment ($40,000)
* r = Annual Interest Rate (8% or 0.08)
* n = Number of Years (25)
**Calculation:**
PV = $40,000 * [1 - (1 + 0.08)^-25] / 0.08
PV = $40,000 * [1 - (1.08)^-25] / 0.08
PV = $40,000 * [1 - 0.1460188] / 0.08
PV = $40,000 * [0.8539812] / 0.08
PV = $40,000 * 10.674765
PV = $426,990.60
**Therefore, you need approximately $426,990.60 in your account at the beginning.**