Compound Interest If 10,000 dollar is invested at an...

Compound Interest If 10,000 dollar is invested at an interest rate of $3 \%$ per year, compounded semiannually, find the value of the investment after the given number of years. $$\begin{array}{llll}{\text { (a) } 5 \text { years }} & {\text { (b) } 10 \text { years }} & {\text { (c) } 15 \text { years }}\end{array}$$

Compound Interest If 10,000 dollar is invested at an interest rate of $3 \%$ per year, compounded semiannually, find the value of the investment after the given number of years.
$$\begin{array}{llll}{\text { (a) } 5 \text { years }} & {\text { (b) } 10 \text { years }} & {\text { (c) } 15 \text { years }}\end{array}$$

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Key Concepts

Compound Interest

Compound interest is the process by which interest earned is reinvested to earn additional interest over time, resulting in exponential growth of the initial investment. It considers the effect of earning interest on both the principal and the accumulated interest.

Compounding Frequency

Compounding frequency refers to the number of times per year that interest is calculated and added to the principal. The frequency (such as semiannual compounding) affects the effective interest rate applied for each period and the overall growth of the investment.

Interest Rate Conversion

When an annual interest rate is provided and compounding occurs more than once per year, it is necessary to convert the annual rate into a periodic rate by dividing it by the number of compounding periods. This conversion ensures accurate calculation of interest for each compounding interval.

Exponential Growth

Exponential growth describes how the value of an investment increases at a rate proportional to its current value due to compound interest. As interest is reinvested, the amount grows faster over time, following an exponential pattern.

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