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An ordinary annuity refers to a series of equal payments made at regular intervals, where the payments occur at the end of each period. It is a fundamental concept in finance used to calculate future values or annuity payments. To find the future value of an ordinary annuity, you use the formula:\[FV = P\frac{(1+r)^n - 1}{r}\]Where:

• \(FV\) is the future value of the annuity.
• \(P\) is the periodic payment or deposit.
• \(r\) is the interest rate per period.
• \(n\) is the total number of compounding periods.

This formula helps determine how much the annuity will grow over time, considering that interest is compounded each period. Understanding and utilizing this formula is crucial when calculating how much your investments will be worth in the future.

Compound interest involves the calculation of interest on an investment's initial principal and the interest that has been added in previous periods. It's the concept of "interest on interest," and is a key component in growing any annuity.In the formula for ordinary annuities, compound interest is accounted for by raising the term \((1 + r)^n\). This expression indicates how the principal grows by compounding the rate per period over the total number of periods. This results in exponential growth which can significantly increase the future value of an annuity.Understanding compound interest is essential when looking at savings and investments because it can maximize your returns over time. Compounding more frequently, such as semiannually instead of annually, can lead to higher returns.

The interest rate per period is a crucial factor in annuity calculations as it directly influences how much your investment will grow over time. Typically, rates are given on an annual basis, so to find the rate per period, you divide the annual interest rate by the number of compounding periods per year.In the given exercise:- The annual interest rate is 9%.- Since the compounding is semiannual, this results in two compounding periods per year.Therefore, the interest rate per period, \(r\), can be calculated as:\[r = \frac{0.09}{2} = 0.045\]This step is vital to correctly apply the ordinary annuity formula and determines how significantly interest affects the future value of an annuity.

The number of compounding periods, \(n\), reflects how often interest is applied over the lifespan of an annuity. It plays an essential role in defining how quickly and substantially your investment grows.To compute \(n\):

• Multiply the number of years by the frequency of compounding per year.
• For the exercise in question: 8 years of investment, compounded semiannually means 16 compounding periods.

The larger the total number of periods, the greater the effect of compounding on the future value. This is because, with each additional compounding period, there's more opportunity for interest to accumulate and grow on itself, augmenting each future payment further.