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Find the amount necessary to fund the given withdrawals.
Semiannual withdrawals of for 9 years; interest rate is compounded semiannually
The amount necessary to fund the given withdrawals is
(Round to the nearest cent as needed.)

Ask by Williams Bowen. in the United States
Mar 20,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The amount necessary to fund the withdrawals is $8,908.25.

Solution

Let the number of compounding periods be
The effective interest rate per period is
Since we have an annuity (a series of payments), the present value is given by
where is the withdrawal amount each period.
Substitute the values into the formula:
First, compute . Notice that
so
Then calculate the numerator:
Next, divide the numerator by :
Finally, multiply by :
Thus, the amount necessary to fund the given withdrawals is

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Mind Expander

To find the amount necessary to fund the semiannual withdrawals, we’ll use the formula for the present value of an annuity. The formula is:
Where:
  • is the present value (amount needed to fund the withdrawals)
  • is the payment amount per period ($650)
  • is the interest rate per period (6.1% annually / 2 = 3.05% or 0.0305)
  • is the total number of payments (9 years * 2 = 18)
Plugging the values into the formula, we get:
Calculating the values step-by-step:
  1. Calculate
  2. Subtract that value from 1.
  3. Divide the result by 0.0305.
  4. Multiply by .
Doing the calculations, you will find:
Therefore, the amount necessary to fund the given withdrawals is approximately:
So, the amount necessary to fund the given withdrawals is .

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