At the end of each quarter, a deposit of $6,000 is made in an account that pays 8% compounded annually. Find the final value at the end of five years

To find the final value of an account with regular quarterly deposits, compounded annually, we can use the **future value of an annuity formula**:

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

where:
- $ P $ is the deposit per period ($6,000 in this case),
- $ r $ is the effective interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Convert the Annual Interest Rate to Quarterly Effective Rate

Since the interest rate is compounded annually but deposits are made quarterly, we'll convert the **8% annual rate** into a quarterly rate, but in this case, the rate remains as an annual rate applied each year. The deposits will be counted as quarterly, with each compounding occurring annually.

Thus, we solve this as an ordinary annuity adjusted for compounding at the end of

At the end of each quarter, a deposit of $6,000 is made in an account that pays 8% compounded annually. Find the final value at the end of five years.

Explore how to calculate the future value of quarterly deposits of $6,000 compounded annually at 8% interest. This example uses the future value of an annuity formula, covering compound interest and periodic deposits over five years. Ideal for high school students in Grades 10-12.

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