Compound Interest If 500 is invested at an interest rate of...

Compound Interest If $\$ 500$ is invested at an interest rate of
3.75$\%$ per year, compounded quarterly, find the value of the
investment after the given number of years.
$$(a)1 \text { year } \quad \text { (b) } 2 \text { years } \quad \text { (c) } 10$$

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Key Concepts

Periodic Compounding

Periodic compounding refers to the frequency at which the accumulated interest is added to the principal. For instance, with quarterly compounding, interest is applied four times per year, which increases the effective rate of growth compared to annual compounding.

Compound Interest

Compound interest is the process of earning interest on both the initial principal and the interest that accumulates over previous periods. This leads to exponential growth of the investment over time and is typically calculated using the compound interest formula.

Interest Rate Conversion

Interest rate conversion is crucial when dealing with non-annual compounding periods. The annual interest rate is adjusted to a periodic rate by dividing it by the number of compounding periods in a year, ensuring that the formula accurately reflects the growth of the investment over each period.

Exponential Growth

Exponential growth in the context of compound interest describes how an investment’s value increases non-linearly because each period’s growth builds upon the previous period's total amount. This exponential behavior significantly accelerates the accumulation of wealth over time.

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