Find the future value of the ordinary annuity. PMT=$7500, i=6% interest compounded semiannually for 9 years

To find the future value of an ordinary annuity, we use the following formula:

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

Where:
- $FV$ is the future value of the annuity
- $PMT$ is the payment made each period
- $i$ is the interest rate per period
- $n$ is the total number of periods

### Given values:
- $PMT = 7500$
- Annual interest rate $r = 6\%$
- Compounded semiannually means we have two periods per year, so:
  \[
  i = \frac{6\%}{2} = 0.03
  \]
- Time $t = 9$ years, so the total number of periods is:
  \[
  n = 9 \times 2 = 18
  \]

### Plugging in the values:
\[
FV = 7500 \times \frac{(1 + 0.03)^{18} - 1}{0.03}
\]

Now let's calculate the future value.The future value of the ordinary annuity is approximately **$175,608.27**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does compounding frequency affect the future value of an annuity?
2. What happens if the payments are made at the beginning of each period (annuity due)?
3. How would the future value change if the interest rate were compounded annually instead of semiannually?
4. What is the difference between future value and present value of an annuity?
5. How can the formula for an ordinary annuity be used in retirement planning?

**Tip**: Always check whether the payments occur at the beginning or end of the period, as it affects the calculation.

Find the future value of the ordinary annuity. PMT=$7500, i=6% interest compounded semiannually for 9 years.

Calculate the future value of an ordinary annuity with $7500 payments, 6% interest compounded semiannually over 9 years. Learn key concepts of interest compounding and future value calculation using the annuity formula. Suitable for advanced high school or college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation