Calculating Compound & Continuous Interest

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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.

Tags

CCSS.7.RP.A.3

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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 continuous compounding?

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Continuous compounding is the process of earning interest on an investment or loan that is calculated and added to the principal continuously, rather than at discrete intervals.

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What is the formula for continuous compounding?

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The formula for continuous compounding is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, e is Euler's number (approximately 2.71828), r is the annual interest rate (decimal), and t is the time in years.

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What does it mean to compound interest monthly?

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Compounding interest monthly means that the interest is calculated and added to the principal balance every month, resulting in interest being earned on previously accumulated interest.

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If you invest $1,000 at an interest rate of 5% compounded annually, how much will you have after 3 years?

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Using the formula A = P(1 + r/n)^(nt), A = 1000(1 + 0.05/1)^(1*3) = $1,157.63.

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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.

Tags

CCSS.7.RP.A.3

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How do you calculate the total amount paid on a loan with compound interest?

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To calculate the total amount paid on a loan with compound interest, use the formula A = P(1 + r/n)^(nt) and then subtract the principal from A to find the interest paid.

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What is the effective annual rate (EAR)?

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The effective annual rate (EAR) is the interest rate on an investment or loan that is compounded over a year, taking into account the effects of compounding.

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How do you find the principal amount needed to reach a specific future value with continuous compounding?

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To find the principal amount needed, rearrange the continuous compounding formula: P = A / e^(rt).