7,900 dollars is placed in a savings account with an annual interest rate of 3%. If no money is added or removed from the account, which equation represents how much will be in the account after 5 years? M=7,900(1.3)^(5) M=7,900(1-0.03)^(5) M=7,900(0.97)^(5) M=7,900(1.03)^(5)

Question

7,900 dollars is placed in a savings account with an annual interest rate of  3%. If no money is added or removed from the account, which equation represents how much will be in the account after 5 years?  M=7,900(1.3)^(5)  M=7,900(1-0.03)^(5)  M=7,900(0.97)^(5)  M=7,900(1.03)^(5)

Bytelearn · Accepted Answer

Compound Interest Formula: To find the amount in the savings account after 5 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. Since the problem does not specify the compounding frequency, we assume it is compounded once per year (n=1). Therefore, the formula simplifies to A = P(1 + r)^t.Given Values: We are given: P = $7,900 (the initial deposit), r = 3% annual interest rate, which as a decimal is 0.03, t = 5 years. We need to plug these values into the simplified compound interest formula A = P(1 + r)^t.Substitute Values: Substituting the given values into the formula, we get: A = 7,900(1 + 0.03)^5 This simplifies to: A = 7,900(1.03)^5 This is the correct representation of the amount in the account after 5 years.

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