Compound Interest

Front

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.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 6.75% becomes 0.0675.

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What is the formula for calculating compound interest?

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The formula for compound interest is 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.

Front

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, r is the annual interest rate (decimal), and t is the time in years.

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If you invest $1,000 at an interest rate of 6.75% compounded semi-annually, how much will you have after 15 years?

Back

$2,706.86

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What does 'compounded annually' mean?

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Compounded annually means that the interest is calculated and added to the principal once a year.

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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.

Front

If the principal is $26,000 and the interest rate is 2.4% compounded continuously for 4 years, what is the total amount owed?

Back

$28,619.74

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What is the effect of increasing the compounding frequency on the total amount?

Back

Increasing the compounding frequency (e.g., from annually to semi-annually or quarterly) generally results in a higher total amount due to interest being calculated more frequently.

Front

How do you calculate the total amount after 15 years if you earn $475 at an interest rate of 3.8% compounded annually?

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$831.10