find the payment made by the ordinary annuity with the given present value 276622 quarterly payments for 27 years intreset rate is 6% compound quartely

To find the payment made by an ordinary annuity, we use the following formula for the present value of an annuity:

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

Where:
- $ PV $ is the present value of the annuity (276,622),
- $ P $ is the periodic payment (what we are solving for),
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Determine values for the formula
- **Present Value (PV):** 276,622
- **Interest rate (r):** Since the interest rate is 6% compounded quarterly, the quarterly rate is:
  \[
  r = \frac{6\%}{4} = 1.5\% = 0.015
  \]
- **Total number of periods (n):** The annuity lasts for 27 years with quarterly payments, so the number of periods is:
  \[
  n = 27 \times 4 = 108
  \]

### Step 2: Solve for $ P $ (the periodic payment)
Rearranging the formula to solve for $ P $:

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

Now, substitute the values into the formula:

\[
P = \frac{276622 \times 0.015}{1 - (1 + 0.015)^{-108}}
\]

Let me calculate that for you.The quarterly payment for the ordinary annuity is approximately **\$5,188.57**.

Would you like more details or have any questions about the solution?

Here are 5 related questions for further exploration:
1. How would the payment change if the interest rate increased to 8%?
2. What is the total amount paid over the 27 years?
3. How would the payment differ for a monthly annuity instead of a quarterly one?
4. What happens to the payment if the annuity lasts for 20 years instead of 27?
5. How is the present value affected if payments are made at the beginning of each period (annuity due)?

**Tip:** When interest is compounded more frequently (e.g., monthly or quarterly), it increases the effective interest rate, which can result in higher total payments over the life of an annuity.

find the payment made by the ordinary annuity with the given present value 276622 quarterly payments for 27 years interest rate is 6% compound quarterly

Learn how to calculate the quarterly payments for an ordinary annuity with a present value of $276,622, 6% annual interest compounded quarterly over 27 years. This step-by-step guide covers the key formulas and mathematical concepts, suitable for advanced high school or college-level students.

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