Suppose that $8000 is invested and pays 4.5% per year under the following compounding options. Determine the total amount in the account after 5 years with each option. a. Compounded annually b. Compounded monthly c. Compounded continuously

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Suppose that $8000 is invested and pays 4.5% per year under the following compounding options. Determine the total amount in the account after 5 years with each option.  a. Compounded annually  b. Compounded monthly  c. Compounded continuously

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Calculate Total Amount Annually: Calculate the total amount for the investment compounded annually. We use the formula for compound interest: A = P(1 + r/n)^(nt), where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money). r = the annual interest rate (decimal). n = the number of times that interest is compounded per year. t = the time the money is invested for, in years.  For annual compounding, n = 1, so the formula simplifies to A = P(1 + r)^t. P = $8000, r = 4.5% or 0.045, t = 5 years.  A = 8000(1 + 0.045)^5 A = 8000(1.045)^5 A = 8000 * 1.246163 A = $9972.90Calculate Total Amount Monthly: Calculate the total amount for the investment compounded monthly. For monthly compounding, n = 12. P = $8000, r = 4.5% or 0.045, t = 5 years.  A = 8000(1 + 0.045/12)^(12*5) A = 8000(1 + 0.00375)^(60) A = 8000(1.00375)^60 A = 8000 * 1.252256 A = $10018.05Calculate Total Amount Continuously: Calculate the total amount for the investment compounded continuously. We use the formula for continuous compounding: A = Pe^(rt), where: e = the base of the natural logarithm, approximately equal to 2.71828. r = the annual interest rate (decimal). t = the time the money is invested for, in years.  P = $8000, r = 4.5% or 0.045, t = 5 years.  A = 8000 * e^(0.045*5) A = 8000 * e^(0.225) A = 8000 * 2.71828^0.225 A = 8000 * 1.252332 A = $10018.66

Suppose that $\$8000$ is invested and pays $4.5\%$ per year under the following compounding options. Determine the total amount in the account after $5$ years with each option. $\newline$ a. Compounded annually $\newline$ b. Compounded monthly $\newline$ c. Compounded continuously

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Suppose that $\$8000$ is invested and pays $4.5\%$ per year under the following compounding options. Determine the total amount in the account after $5$ years with each option. $\newline$ a. Compounded annually $\newline$ b. Compounded monthly $\newline$ c. Compounded continuously