A contract requires lease payments of $900 at the beginning of every month for 3 years.

**a.** What is the present value of the contract if the lease rate is 4.75% compounded annually DO NOT ROUND FIGURES WHILE CALCULATING

To calculate the present value (PV) of the contract, we'll use the formula for the present value of an annuity due (payments made at the beginning of each period):

\[
PV = R \times \left( \frac{1 - (1 + i)^{-n}}{i} \right) \times (1 + i)
\]

where:
- $ R = 900 $ (monthly payment),
- $ i $ is the monthly interest rate,
- $ n = 36 $ (number of monthly payments over 3 years).

Since the lease rate is 4.75% compounded annually, we need to convert it to an effective monthly rate.

### Step 1: Calculate the Monthly Interest Rate

The annual rate $ r = 4.75\% $, so the monthly rate $ i $ is:

\[
i = \left(1 + \frac{r}{1}\right)^{\frac{1}{12}} - 1
\]
\[
i = \left(1 + 0.0475\right)^{\frac{1}{12}} - 1
\]

Calculating this gives the effective monthly rate $ i $.

### Step 2: Plug Values into the Formula

Once we have $ i $, substitute into the formula with $ n = 36 $, and solve for $ PV $. 

Let me perform the calculations.The present value of the contract, with lease payments of $900 at the beginning of every month for 3 years at a 4.75% interest rate compounded annually, is approximately **$30,304.29** (without rounding intermediate figures).

Would you like a breakdown of the steps? 

Here are some related questions:
1. How would the present value change if payments were made at the end of each month?
2. What would be the effect on PV if the lease rate was compounded monthly instead of annually?
3. How does the present value change if the interest rate increases to 5%?
4. What is the formula for calculating the future value of an annuity due?
5. How would you calculate the total interest paid over the lease period?

**Tip:** For annuity due problems, remember to multiply by $(1 + i)$ at the end to account for payments made at the beginning of each period.

A contract requires lease payments of $900 at the beginning of every month for 3 years.

**a.** What is the present value of the contract if the lease rate is 4.75% compounded annually DO NOT ROUND FIGURES WHILE CALCULATING

Calculate the present value of a lease contract with payments of $900 at the beginning of every month over 3 years, given a 4.75% annual interest rate compounded annually. Learn how to find the effective monthly interest rate and apply the annuity due formula without rounding intermediate values. Ideal for advanced high school and college students.

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