The maker of cardboard boxes leases a warehouse and pays $9,000 at the beginning of each month for 5 years. If interest rates are 2.25% compounded monthly, what is the present value (in dollars) of the payments? (Round your answer to the nearest cent.)

To find the present value of the monthly payments, we can use the formula for the present value of an annuity:

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

where:
- $PV$ is the present value (what we are solving for),
- $P$ is the monthly payment (\$9,000),
- $r$ is the monthly interest rate (which is the annual interest rate divided by 12),
- $n$ is the total number of payments.

### Given:
- The monthly payment, $P = 9000$,
- The annual interest rate is 2.25%, so the monthly interest rate, $r = \frac{2.25\%}{12} = \frac{0.0225}{12} = 0.001875$,
- The number of months in 5 years is $n = 5 \times 12 = 60$.

Now, we can calculate the present value using these values.The present value of the monthly payments is approximately **$510,280.89**.

Would you like further details or have any other questions?

Here are 5 related questions for further practice:
1. What would be the present value if the interest rate were 3% compounded monthly?
2. How would the present value change if the monthly payment was $10,000 instead of $9,000?
3. What is the total amount paid over 5 years without considering the present value?
4. How would the calculation change if the payments were made at the end of each month?
5. How does the present value change if the number of years increases to 10 years?

**Tip:** When working with interest rates, always ensure the correct compounding period is used in calculations (e.g., monthly vs. annually).

Calculate the present value of monthly payments for a warehouse lease of $9,000 at the beginning of each month over 5 years, with a 2.25% compounded monthly interest rate. Learn how to apply the present value annuity formula for accurate financial analysis.

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