To calculate the present value (PV) of the monthly lease payments, we can use the Present Value of an Annuity Due formula because the payments are made at the beginning of each month.

The formula for the Present Value of an Annuity Due is:

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

Where:

• $P$ = monthly payment ($7,000)
• $r$ = monthly interest rate = annual rate / 12 = $3.75\% / 12 = 0.003125$
• $n$ = total number of payments = 5 years × 12 months = 60 months

Step-by-Step Calculation:

1. Monthly payment $P = 7,000$
2. Monthly interest rate $r = 0.003125$
3. Total number of payments $n = 60$

Now we substitute these values into the formula:

$PV = 7,000 \times \frac{1 - (1 + 0.003125)^{-60}}{0.003125} \times (1 + 0.003125)$

Let’s compute this.

$(1 + 0.003125)^{-60} \approx 0.835645$

Now, calculate the fraction:

$\frac{1 - 0.835645}{0.003125} \approx 52.49904$

Next, multiply by $P$ and the adjustment factor $(1 + r)$:

$7,000 \times 52.49904 \times 1.003125 \approx 7,000 \times 52.627 \approx 368,389.12$

So, the present value of the payments is approximately $368,389.12.

Final Answer:

The present value of the payments is $368,389.12.

Would you like further clarification on this solution, or do you have any more questions? Here are a few related questions to help:

1. What is the difference between an annuity due and an ordinary annuity?
2. How does the interest rate impact the present value of annuity payments?
3. How would the present value change if the interest rate were 5% instead of 3.75%?
4. What if the payments were made at the end of each month instead of the beginning? How would that change the formula?
5. Can the present value of an annuity be calculated if payments are irregular (i.e., the payment amount changes every period)?

Tip: When calculating the present value of annuities, always ensure you are using the correct interest rate for the payment frequency (e.g., monthly, quarterly, etc.).