Calculate, to the nearest cent, the future value of an...

Calculate, to the nearest cent, the future value of an investment of $\$ 10,000$ at the stated interest rate after the stated amount of time. [HINT: See Quick Examples 1 and $2 .$.
$2.5 \%$ per year, compounded quarterly (4 times per year), after 5 years

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Key Concepts

Compound Interest

Compound interest is the process of calculating interest not only on the initial principal but also on the accumulated interest from previous periods. This results in exponential growth of the investment over time and is calculated using an exponent that reflects the number of compounding periods.

Periodic Interest Rate

The periodic interest rate is derived by converting the annual interest rate to a rate that applies to each compounding period. This involves dividing the annual rate by the number of compounding periods in a year to accurately compute the interest accrued in each period.

Compounding Frequency

Compounding frequency refers to the number of times per year that the accumulated interest is calculated and added to the principal. A higher compounding frequency results in more frequent application of interest, thereby impacting the overall growth of the investment.

Future Value Calculation

Future value calculation involves the use of the compound interest formula, which incorporates the initial principal, the periodic interest rate, and the total number of compounding periods. This formula allows for the determination of the accumulated value of an investment after a certain period of time.

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