SOLUTION: Scarlett has $700,000 saved for retirement in an account earning 3.95% interest, compounded weekly. How much will she be able to withdraw each week if she wants to take withdrawals

Algebra ->  Expressions -> SOLUTION: Scarlett has $700,000 saved for retirement in an account earning 3.95% interest, compounded weekly. How much will she be able to withdraw each week if she wants to take withdrawals      Log On


   

Question 1209862: Scarlett has $700,000 saved for retirement in an account earning 3.95% interest, compounded weekly. How much will she be able to withdraw each week if she wants to take withdrawals for 23 years? Round your answer to the nearest dollar.
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to calculate the weekly withdrawal amount:
**1. Convert Annual Interest Rate to Weekly Rate:**
* Annual interest rate: 3.95% = 0.0395
* Weekly interest rate: 0.0395 / 52 weeks ≈ 0.00076
**2. Calculate the Total Number of Withdrawals:**
* Withdrawal period: 23 years
* Total withdrawals: 23 years * 52 weeks/year = 1196 weeks
**3. Use the Present Value of an Ordinary Annuity Formula:**
* This formula helps determine the regular withdrawal amount from a present lump sum, considering compound interest.
* The formula is: PMT = PV \* \[r(1 + r)^n] / \[(1 + r)^n - 1]
* PMT = Payment (weekly withdrawal)
* PV = Present Value ($700,000)
* r = Weekly interest rate (0.00076)
* n = Number of withdrawals (1196)
**4. Plug in the Values and Calculate:**
* PMT = $700,000 \* \[0.00076(1 + 0.00076)^1196] / \[(1 + 0.00076)^1196 - 1]
* PMT ≈ $891
**Answer:** Scarlett will be able to withdraw approximately $891 each week.