A business sets up a sinking fund so they will have a $48,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in the investment that pays 7.2% compounded every 2 months, what size should each payment be?

The every 2 months payments are $

To determine the size of each payment, we can use the formula for the future value of an ordinary annuity, which is:

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

Where:
- $FV$ is the future value (amount they want, $48,000),
- $P$ is the payment amount per period (this is what we're solving for),
- $i$ is the interest rate per period,
- $n$ is the total number of periods.

### Step 1: Find the values for the variables
- $FV = 48,000$,
- The investment is for 9 years, and payments are made every 2 months. There are 6 two-month periods in a year, so:
  \[
  n = 9 \times 6 = 54 \text{ periods}
  \]
- The annual interest rate is 7.2%, compounded every 2 months, so:
  \[
  i = \frac{7.2\%}{6} = \frac{0.072}{6} = 0.012 \text{ per period}
  \]

### Step 2: Plug values into the formula

\[
48,000 = P \times \frac{{(1 + 0.012)^{54} - 1}}{0.012}
\]

Now, let's solve for $P$. I'll calculate that.The size of each payment should be approximately **$636.92**.

Would you like more details on the calculation, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. How would the payment change if the interest rate were compounded monthly?
2. What would be the required payment if the equipment cost $60,000 instead of $48,000?
3. How does increasing the frequency of payments affect the total interest earned?
4. What would happen to the payment size if the time frame were reduced to 7 years?
5. How much total interest will be earned over the 9-year period?

**Tip:** When interest is compounded more frequently, the payment per period generally decreases.

A business sets up a sinking fund so they will have $48,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in an investment that pays 7.2% compounded every 2 months, what size should each payment be?

Learn how to calculate the payment size for a sinking fund where $48,000 is needed in 9 years with an interest rate of 7.2% compounded every 2 months. This problem covers financial concepts such as the future value of ordinary annuities and compound interest.

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