A business sets up a sinking fund so they will have a $45,000.00 to pay for a replacement piece of equipment in 7 years when the current equipment will be sold for scrap. If they make deposits at the end of each month for 7 years in the investment that pays 7.6% compounded monthly, what size should each payment be?

The monthly payments are $

To find the size of each monthly payment, we use the formula for the future value of a sinking fund with regular payments and compound interest. The formula is:

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

Where:
- $ FV $ is the future value (the amount they want in the fund, which is $45,000),
- $ P $ is the monthly payment (which we are solving for),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments (number of months).

### Step 1: Find the monthly interest rate
The annual interest rate is 7.6%, so the monthly interest rate is:

\[
r = \frac{7.6\%}{12} = \frac{0.076}{12} = 0.0063333
\]

### Step 2: Calculate the total number of payments
The equipment will be replaced in 7 years, and payments are made monthly, so:

\[
n = 7 \times 12 = 84 \text{ months}
\]

### Step 3: Plug into the formula
We want to solve for $ P $:

\[
45000 = P \times \frac{(1 + 0.0063333)^{84} - 1}{0.0063333}
\]

Let's calculate this.The monthly payment required to reach $45,000 in 7 years, with a 7.6% interest rate compounded monthly, is approximately **$407.45**.

Would you like more details or have any questions about this process?

Here are 5 related questions to consider:
1. How does changing the interest rate affect the payment size?
2. What if the company wanted to replace the equipment in 5 years instead of 7 years?
3. How does compound interest differ from simple interest in this context?
4. What happens if payments are made at the beginning of each month instead of the end?
5. How would the monthly payment change if they need $60,000 instead of $45,000?

**Tip:** Always make sure to check whether interest is compounded monthly, quarterly, or annually, as this affects the payment calculations significantly.

A business sets up a sinking fund so they will have a $45,000.00 to pay for a replacement piece of equipment in 7 years when the current equipment will be sold for scrap. If they make deposits at the end of each month for 7 years in the investment that pays 7.6% compounded monthly, what size should each payment be?

Calculate the monthly payments needed to reach $45,000 in a sinking fund over 7 years with 7.6% interest compounded monthly. Learn about the sinking fund formula, compound interest calculations, and financial planning techniques. Suitable for advanced high school or college-level students.

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