9,900 dollars is placed in a savings account with an annual interest rate of 1.7%. If no money is added or removed from the account, which equation represents how much will be in the account after 8 years? M=9,900(0.017)^(8) M=9,900(1.017)^(8) M=9,900(1+0.017)(1+0.017)(1+0.017)(1+0.017) M=9,900(0.983)^(8)

Question

9,900 dollars is placed in a savings account with an annual interest rate of  1.7%. If no money is added or removed from the account, which equation represents how much will be in the account after 8 years?  M=9,900(0.017)^(8)  M=9,900(1.017)^(8)  M=9,900(1+0.017)(1+0.017)(1+0.017)(1+0.017)  M=9,900(0.983)^(8)

Bytelearn · Accepted Answer

Use Compound Interest Formula: To find the total amount in the account after 8 years with compound interest, we use the formula for compound interest: 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 time the money is invested for in years.Identify Given Values: In this problem, P = $9,900, r = 1.7% or 0.017 as a decimal, n = 1 (since the interest is compounded annually), and t = 8 years. We need to plug these values into the compound interest formula.Substitute Values: Substituting the given values into the compound interest formula, we get A = 9,900(1 + 0.017/1)^(1*8).Simplify Equation: Simplify the equation to get A = 9,900(1 + 0.017)^(8).Final Account Amount: Further simplifying, we get A = 9,900(1.017)^(8). This is the correct equation that represents how much will be in the account after 8 years.

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