Question\begin{tabular}{|c|} \hline Compound Interest Applications \\ \hline Solve the following compound interest problems. Round your results to the nearest cent as needed. \\ \hline \begin{tabular}{l} Michael invests for 3 years at an interest rate of compounded quarterly. Determine the interest he will earn at the end of 3 years. \\ Michael will earn in interest on his investment. \\ dollars \end{tabular} \\ \hline \begin{tabular}{l} Maureen takes out a loan with a compound interest rate of . If Maureen borrows for 11 years compounded monthly, how much interest will she pay at the end of 11 years? \\ Maureen will pay back \\square$ in interest on her loan. \\ dollars \end{tabular} \\ \hline \end{tabular}
Studdy Solution
STEP 1
1. We are using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
2. Interest earned or paid is the difference between the final amount and the principal.
3. Results should be rounded to the nearest cent.
4. For quarterly compounding, n = 4.
5. For monthly compounding, n = 12.
6. Interest rates are given as percentages and need to be converted to decimals.
STEP 2
1. Solve Michael's investment problem.
2. Solve Maureen's loan problem.
STEP 3
Let's start with Michael's investment:
P = $3000
r = 6% = 0.06
n = 4 (compounded quarterly)
t = 3 years
Using the compound interest formula:
A = 3000(1 + 0.06/4)^(4*3)
A = 3000(1.015)^12
STEP 4
Calculate the final amount for Michael's investment:
A = 3000(1.015)^12
A = 3000 * 1.1946947
A = $3584.0841
Now, calculate the interest earned:
Interest = Final Amount - Principal
Interest = 3584.0841 - 3000
Interest = $584.0841
Rounding to the nearest cent:
Interest = $584.09
STEP 5
Now let's solve Maureen's loan problem:
P = $4000
r = 14% = 0.14
n = 12 (compounded monthly)
t = 11 years
Using the compound interest formula:
A = 4000(1 + 0.14/12)^(12*11)
A = 4000(1.011666667)^132
STEP 6
Calculate the final amount for Maureen's loan:
A = 4000(1.011666667)^132
A = 4000 * 4.5771675
A = $18308.67
Now, calculate the interest paid:
Interest = Final Amount - Principal
Interest = 18308.67 - 4000
Interest = $14308.67
Rounding to the nearest cent:
Interest = $14308.67
Maureen will pay back $14308.67 in interest on her loan.
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