Continuous Compounded Interest

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What is Continuous Compounding?

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Continuous compounding is the process of earning interest on an investment where the interest is calculated and added to the principal continuously, rather than at discrete intervals. The formula used is A = Pe^(rt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and t is the time in years.

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What is the formula for calculating the future value with continuous compounding?

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The formula for calculating future value with continuous compounding is A = Pe^(rt), where A is the future value, P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years.

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If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

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$2,225.54

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What is the difference between compounded annually and compounded continuously?

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Compounded annually means interest is calculated and added to the principal once a year, while compounded continuously means interest is calculated and added to the principal at every possible moment.

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How do you convert a percentage to a decimal for calculations?

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To convert a percentage to a decimal, divide the percentage by 100. For example, 16% becomes 0.16.

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What is the effective annual rate (EAR) for an investment compounded continuously?

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The effective annual rate (EAR) for an investment compounded continuously can be calculated using the formula EAR = e^r - 1, where r is the nominal interest rate.

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If Caiden earned $475 and deposited it at 3.8% interest compounded annually, what will be his balance after 15 years?

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$831.10

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What is the formula for calculating the future value of a series of monthly deposits?

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The future value of a series of monthly deposits can be calculated using the formula FV = P * [(1 + r/n)^(nt) - 1] / (r/n), where P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

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If Fong puts $150 into an account every month at 3.5% interest compounded monthly, how much will he have in 8 years?

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$16,590.38

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What is the total amount paid on a loan with 9.5% interest compounded quarterly after 8 years if the principal is $7,400?

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$15,683.28