Find the amount of each payment to be made into sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given as per period. $75,000; money earns 4.8% compounded quarterly for 1 2/3 years

To find the amount of each payment to be made into a sinking fund, we can use the future value of an ordinary annuity formula. The payments are made at the end of each period, and the money earns interest compounded quarterly. The formula is:

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

Where:
- $A$ is the future value of the sinking fund (in this case, $75,000),
- $P$ is the payment per period (which we need to find),
- $i$ is the interest rate per period,
- $n$ is the total number of payments.

### Step 1: Identify the known values
- **Future value**: $A = 75,000$
- **Annual interest rate**: $4.8\%$, compounded quarterly.
- **Interest rate per period**: $i = \frac{4.8\%}{4} = 1.2\%$ or $0.012$ per period.
- **Number of periods**: 1 2/3 years = $1 + \frac{2}{3} = \frac{5}{3}$ years.

Since payments are made quarterly, the number of periods is:

\[
n = 4 \times \frac{5}{3} = \frac{20}{3} = 6.67 \approx 7 \text{ periods}.
\]

### Step 2: Plug the values into the formula
We need to solve for $P$:

\[
75,000 = P \cdot \frac{(1 + 0.012)^7 - 1}{0.012}
\]

Now let's compute the value of $P$.The amount of each payment to be made into the sinking fund is approximately **$10,334.71** per quarter.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How does the payment change if the interest rate is 6% instead of 4.8%?
2. What if the payments were made monthly instead of quarterly?
3. How would the total amount change if the duration was extended to 2 years?
4. What is the total amount of interest earned over the period?
5. How would this formula change if the payments were made at the beginning of each period?

**Tip:** Always check how frequently interest compounds, as it significantly affects the amount needed for periodic payments.

Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given as per period. $75,000; money earns 4.8% compounded quarterly for 1 2/3 years.

Calculate the quarterly payments required to accumulate $75,000 in a sinking fund with an interest rate of 4.8% compounded quarterly for 1 2/3 years. Learn how to use the future value of an ordinary annuity formula to solve this financial math problem.

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