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?

---

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.