Compound interest and exponential functions Characteristics

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What is compound interest?

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Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

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How is compound interest calculated?

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Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

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What is the difference between simple interest and compound interest?

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Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

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What does it mean for an investment to double in size?

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An investment doubles in size when its value becomes twice the original amount, often described in terms of the time it takes for this to happen, known as the doubling time.

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What is exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

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What is the formula for exponential decay?

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The formula for exponential decay is A = A0 * e^(-kt), where A0 is the initial amount, k is the decay constant, and t is time.

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How do you convert a percentage to a decimal?

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To convert a percentage to a decimal, divide the percentage by 100.

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What is depreciation in financial terms?

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Depreciation is the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

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What is the formula for calculating the future value of an investment with depreciation?

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The future value of an investment with depreciation can be calculated using the formula FV = PV * (1 - r)^t, where FV is the future value, PV is the present value, r is the depreciation rate, and t is the time in years.

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What is the significance of the interest rate in compound interest?

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The interest rate determines how much interest is earned on the principal amount and affects the total amount accumulated over time.