Kimberlé is going to finance new office equipment at a 2% rate over a 3.5 year term. If she can afford monthly payments of $200, how much can she pay for the new office equipment? Round your answer to the nearest dollar.

We can solve this problem by using the formula for the present value of an annuity, which is commonly used in loan and finance calculations:

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

Where:
- $PV$ is the present value (the amount Kimberlé can afford to finance),
- $P$ is the monthly payment ($200),
- $r$ is the monthly interest rate,
- $n$ is the total number of payments.

### Step 1: Convert the annual interest rate to a monthly interest rate
Since the annual interest rate is 2%, the monthly interest rate will be:

\[
r = \frac{2\%}{12} = 0.02 \div 12 = 0.00167
\]

### Step 2: Calculate the number of months in the loan term
Kimberlé is financing over 3.5 years, so the total number of months is:

\[
n = 3.5 \times 12 = 42 \text{ months}
\]

### Step 3: Plug values into the formula
Now, using the formula for the present value of an annuity:

\[
PV = 200 \times \frac{1 - (1 + 0.00167)^{-42}}{0.00167}
\]

I'll calculate this step for you.Kimberlé can afford to finance approximately $8,106 for the new office equipment.

Do you need more details or have any questions? Here are some related questions to further explore:

1. What happens to the amount she can finance if the interest rate increases to 3%?
2. How much would her monthly payment need to be if she wants to finance $10,000 instead?
3. How does the term length affect the monthly payments if the total financed amount stays the same?
4. What is the total amount of interest Kimberlé will pay over the term?
5. How does financing with monthly payments compare to making a lump sum payment in terms of cost?

**Tip:** When calculating loans, always remember to distinguish between nominal (annual) and effective (monthly) interest rates, as this can affect your results.

Learn how to calculate the present value of annuity for financing new office equipment at a 2% interest rate over 3.5 years. Kimberlé can afford $200 in monthly payments, and we'll determine how much she can finance using step-by-step calculations and the present value of annuity formula.

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