Amount of annuity expected $900. Payment annually. Time 4 years. Rate 6%. What’s the present value needed to invest to receive annuity

To find the **present value (PV)** of an annuity with regular payments, we use the **Present Value of Annuity Formula**:  

\[
PV = P \times \left(1 - (1 + r)^{-n}\right) \div r
\]

Where:  
- $PV$ = Present value of the annuity  
- $P$ = Payment per period ($900)  
- $r$ = Interest rate per period (6% or 0.06)  
- $n$ = Total number of periods (4 years)

### Step-by-Step Calculation:

1. **Input values:**  
   - $P = 900$  
   - $r = 0.06$  
   - $n = 4$

2. **Calculate $(1 + r)^{-n}$:**  
   \[
(1 + 0.06)^{-4} = 1.06^{-4} \approx 0.7921
   \]

3. **Calculate $1 - (1.06)^{-4}$:**  
   \[
1 - 0.7921 = 0.2079
   \]

4. **Divide by the interest rate $r = 0.06$:**  
   \[
\frac{0.2079}{0.06} \approx 3.465
   \]

5. **Multiply by the annual payment $P = 900$:**  
   \[
PV = 900 \times 3.465 \approx 3,118.5
   \]

### Final Answer:
The **present value** needed to invest to receive a $900 annuity for 4 years at a 6% annual interest rate is approximately:

\[
\boxed{3,118.50}
\]

Would you like more details, or do you have any follow-up questions?

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### 5 Related Questions:
1. How would the present value change if the interest rate was 8%?
2. What if the payments were made monthly instead of annually?
3. How is present value affected if the time period increases to 6 years?
4. What formula would you use for the **future value** of an annuity?
5. How does inflation impact the value of annuities over time?

---

### Tip:
The **present value of an annuity** helps you understand how much you need to invest today to achieve specific financial goals with recurring payments.

Amount of annuity expected $900. Payment annually. Time 4 years. Rate 6%. What’s the present value needed to invest to receive annuity?

Calculate the present value of an annuity of $900 paid annually over 4 years with a 6% interest rate. Learn the step-by-step process using the present value of annuity formula. This problem covers concepts in the time value of money and annuities, suitable for Grades 10-12.

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