Find the amount needed to deposit into an account today that will yield a typical pension payment of $20,000 at the end of each of the next 26 years for the given annual interest rate. (Round your answer to the nearest cent.)

8.1%

To find the amount that needs to be deposited today to yield $20,000 at the end of each of the next 26 years with an annual interest rate of 8.1%, we can use the **Present Value of an Annuity formula**:

\[
PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}
\]

where:
- $ PV $ is the present value (the amount to be deposited today),
- $ PMT $ is the annual payment ($20,000),
- $ r $ is the annual interest rate (8.1%, or 0.081 as a decimal),
- $ n $ is the number of years (26).

### Step-by-Step Calculation

1. **Convert the interest rate**:
   \[
   r = 0.081
   \]

2. **Plug in the values**:
   \[
   PV = 20000 \times \frac{1 - (1 + 0.081)^{-26}}{0.081}
   \]

3. **Calculate $ (1 + r)^{-n} $**:
   \[
   (1 + 0.081)^{-26} \approx 0.117254
   \]

4. **Calculate the entire fraction**:
   \[
   \frac{1 - 0.117254}{0.081} \approx 10.896
   \]

5. **Multiply by the payment amount**:
   \[
   PV \approx 20000 \times 10.896 = 217,920
   \]

So, the amount needed to deposit today is approximately **$217,920.00**.

Would you like further clarification on any steps? 

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### Related Questions:
1. How would the required deposit change if the interest rate were higher, say 10%?
2. What if the interest rate were compounded monthly instead of annually?
3. How would changing the annual payment to $25,000 affect the required deposit?
4. What is the effect of increasing the term to 30 years instead of 26?
5. How can the Present Value of an Annuity formula be derived?

### Tip:
Always remember to convert percentage rates into decimal form in formulas.

Find the amount needed to deposit into an account today that will yield a typical pension payment of $20,000 at the end of each of the next 26 years for the given annual interest rate. (Round your answer to the nearest cent.)

8.1%

Learn to calculate the amount to deposit today to yield $20,000 annual pension payments over 26 years at an 8.1% interest rate. This solution demonstrates the Present Value of an Annuity formula, covering essential time value of money principles. Ideal for finance students or anyone interested in retirement planning.

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