Compound and Continuous Interest

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What is simple interest?

Back

Simple interest is calculated using the formula: I = PRT, where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years.

Tags

CCSS.7.RP.A.3

Front

What is compound interest?

Back

Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal, 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.

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What is the difference between simple and compound interest?

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The main difference is that 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.HSF.BF.A.2

Front

How do you calculate the future value with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Front

What is continuous compounding?

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Continuous compounding is the process of earning interest on interest continuously, rather than at discrete intervals. The formula is A = Pe^(rt), where A is the amount, P is the principal, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

Front

How do you calculate the ending balance for continuous compounding?

Back

Use the formula A = Pe^(rt), where A is the ending balance, P is the principal amount, e is approximately 2.71828, r is the annual interest rate, and t is the time in years.

Front

What is the formula for calculating compound interest when compounded monthly?

Back

The formula is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year (12 for monthly), and t is the number of years.

Front

If $1,000 is invested at 5% interest compounded annually for 3 years, what is the future value?

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A = 1000(1 + 0.05/1)^(1*3) = $1,157.63.

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What is the effect of increasing the compounding frequency on the amount of interest earned?

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Increasing the compounding frequency (e.g., from annually to monthly) results in more interest being earned, as interest is calculated and added to the principal more frequently.

Front

What is the principal in the context of interest calculations?

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The principal is the initial amount of money that is invested or loaned, before any interest is added.