An investor deposits $5,000 into an investment account that offers a nominal annual interest rate of 8%. Consider an investment period of 10 years.
(a) Calculate the final amount if the interest is compounded annually.
(b) Calculate the final amount if the interest is compounded quarterly.
(c) Compare the final amounts from parts (a) and (b). Explain how the compounding frequency affects the accumulated interest and suggest which compounding method is more beneficial for the investor.
Question
Calculate the final amount after 10 years for a $5,000 principal with a nominal annual interest rate of 8% compounded annually.
Hint
Hint
Hint
Use the annual compound interest formula: \(A = P(1 + r)^t\).
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Answer
Answer
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Explanation
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- Formula Booklet
Complete Answer
$10,794.62
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Question
Calculate the final amount for the same investment when the interest is compounded quarterly.
Hint
Hint
Hint
Adjust the formula for quarterly compounding: \(A = P\left(1 + \frac{r}{n}\right)^{nt}\), where \(n=4\) for quarterly compounding.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
$11,040.20
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Question
Compare the outcomes from parts (a) and (b) and explain how the change in compounding frequency affects the final amount. Which compounding method is more beneficial for the investor?
Hint
Hint
Hint
Consider the effective interest rate and how more frequent compounding impacts the growth of the investment.
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Answer
Answer
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Explanation
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- Formula Booklet
Complete Answer
Quarterly compounding yields a higher final amount ($11,040.20) compared to annual compounding ($10,794.62). More frequent compounding is more beneficial for the investor because interest is calculated and added to the principal more often, leading to a greater accumulation of interest over time due to the interest-on-interest effect. Thus, quarterly compounding is more beneficial.
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