Calculating Compound & Continuous Interest

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What is compound interest?

Back

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 annually?

Back

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

Front

What is continuous interest?

Back

Continuous interest is calculated using the formula A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the annual interest rate, and e is Euler's number (approximately 2.71828).

Front

What is the formula for calculating compound interest?

Back

The formula for calculating compound interest is A = P(1 + r/n)^(nt).

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What does 'compounded quarterly' mean?

Back

Compounded quarterly means that the interest is calculated and added to the principal four times a year.

Front

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

Back

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

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated interest.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the total interest paid on a loan?

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Total interest paid can be found by subtracting the principal from the total amount paid: Total Interest = Total Amount - Principal.

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What is the effect of increasing the interest rate on compound interest?

Back

Increasing the interest rate results in a higher total amount accumulated over time due to more interest being earned on both the principal and accumulated interest.

Front

How long will it take for an investment to double at a 7% interest rate compounded annually?

Back

Using the Rule of 72, divide 72 by the interest rate: 72 / 7 = approximately 10.29 years.

Tags

CCSS.HSF.LE.A.4