Compound Interest Formula and Compounding Continuously

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What is the formula for 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 (the initial amount of money), 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 the money is invested or borrowed.

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What does 'compounded continuously' mean?

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Compounding continuously means that the interest is calculated and added to the principal at every possible instant. The formula used 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, and e is Euler's number (approximately 2.71828).

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How do you calculate the total amount after 8 years with continuous compounding?

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Using the formula A = Pe^(rt), if P = 3250, r = 0.062, and t = 8, then A = 3250e^(0.062*8) which calculates to approximately $3250e^{0.496}.

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What is the difference between annual compounding and continuous compounding?

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Annual compounding calculates interest once per year, while continuous compounding calculates interest at every moment, leading to a higher total amount due to more frequent interest calculations.

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If you invest $5,000 at 4% interest compounded annually, what is the value after 3 years?

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Using the formula A = P(1 + r)^t, A = 5000(1 + 0.04)^3 = 5000(1.124864) = $5,624.32.

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What does 'semi-annually' mean in terms of compounding?

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Semi-annually means that interest is compounded twice a year.

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How do you determine which investment has a larger balance after a set period?

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To determine which investment has a larger balance, calculate the future value of each investment using the appropriate compounding formula and compare the results.

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What is the formula for calculating the future value of an investment compounded monthly?

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The formula is A = P(1 + r/n)^(nt), where n is the number of compounding periods per year (12 for monthly).

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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 effect of compounding. It can be calculated using the formula: EAR = (1 + r/n)^(nt) - 1.

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How do you calculate the amount of an investment compounded daily?

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Use the formula A = P(1 + r/n)^(nt), where n is 365 for daily compounding.