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Sally's investment of $7980 earns interest at 5% per year. compounded quarterly over 7 years. What is the amount of interest earned? Write your answer to the nearest cent.

Sally's investment of $7980\$7980 earns interest at 5%5\% per year. compounded quarterly over 77 years.\newline What is the amount of interest earned? \newlineWrite your answer to the nearest cent.

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Full solution

Q. Sally's investment of $7980\$7980 earns interest at 5%5\% per year. compounded quarterly over 77 years.\newline What is the amount of interest earned? \newlineWrite your answer to the nearest cent.
  1. Identify Formula: Identify the formula for compound interest.\newlineCompound Interest Formula: A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}\newlineWhere:\newlinePP = principal amount ($\$\(7980\))\(\newline\)\(r\) = annual interest rate (\(5\%\) or \(0.05\))\(\newline\)\(n\) = number of times interest applied per time period (\(4\), since quarterly)\(\newline\)\(t\) = time the money is invested for in years (\(7\))
  2. Plug Values: Plug the values into the formula to calculate the final amount.\(\newline\)\(A = 7980(1 + 0.05/4)^{4\times7}\)\(\newline\)\(A = 7980(1 + 0.0125)^{28}\)\(\newline\)\(A = 7980(1.0125)^{28}\)
  3. Calculate Power: Calculate the power \((1.0125)^{28}\).\((1.0125)^{28} \approx 1.4116\)
  4. Multiply Principal: Multiply the principal amount by the result from Step \(3\).\(\newline\)\(A = 7980 \times 1.4116\)\(\newline\)\(A \approx 11268.57\)
  5. Calculate Interest: Calculate the interest earned by subtracting the principal from the final amount.\(\newline\)\(\text{Interest} = \text{Final Amount} - \text{Principal}\)\(\newline\)\(\text{Interest} = 11268.57 - 7980\)\(\newline\)\(\text{Interest} \approx 3288.57\)

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