7,900 dollars is placed in a savings account with an annual interest rate of 6%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years? M=7,900(1.06)^(6) M=7,900(0.06)^(6) M=7,900(1+0.06)(1+0.06)(1+0.06) M=7,900(1-0.06)^(6)

Question

7,900 dollars is placed in a savings account with an annual interest rate of  6%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years?  M=7,900(1.06)^(6)  M=7,900(0.06)^(6)  M=7,900(1+0.06)(1+0.06)(1+0.06)  M=7,900(1-0.06)^(6)

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Problem Explanation: The problem involves calculating the future value of a single lump sum investment using compound interest. The general formula for compound interest is: 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. In this case, the interest is compounded annually (n=1), so the formula simplifies to: A = P(1 + r)^tCompound Interest Formula: We are given: P = $7,900 (the initial deposit) r = 6% annual interest rate, which as a decimal is 0.06 t = 6 years We need to substitute these values into the simplified compound interest formula.Substitution of Values: Substituting the given values into the formula, we get: A = 7,900(1 + 0.06)^6 This equation correctly represents the amount of money in the account after 6 years, including the compounded annual interest.Comparison with Options: Now let's examine the provided options to identify which one matches our derived equation: M=7,900(1.06)^(6) - This option correctly applies the compound interest formula. M=7,900(0.06)^(6) - This option incorrectly uses only the interest rate without adding 1, which is not how compound interest is calculated. M=7,900(1+0.06)(1+0.06)(1+0.06) - This option seems to be attempting to represent compound interest without using exponents, but it only multiplies the factor three times instead of six. M=7,900(1-0.06)^(6) - This option incorrectly subtracts the interest rate from 1, which would represent a depreciation, not compound interest.

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