Multiple choice

An individual invests $5,000 in three different investment schemes for one year. Scheme A offers a fixed interest rate of 9% per annum, Scheme B offers a compound interest rate of 8% per annum calculated semi-annually, and Scheme C offers a compound interest rate of 8% per annum calculated quarterly. Which scheme would yield the highest return on the investment after one year?

  1. Scheme A

  2. Scheme B

  3. Scheme C

  4. All the above Scheme provide same return.
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A Correct answer
Explanation

Scheme A: 9% simple interest = 5000 * 0.09 = 450. Scheme B: 8% compounded semi-annually = 5000 * (1 + 0.04)^2 - 5000 = 5000 * 1.0816 - 5000 = 408. Scheme C: 8% compounded quarterly = 5000 * (1 + 0.02)^4 - 5000 = 5000 * 1.0824 - 5000 = 412. Scheme A yields the highest return.

AI explanation

Using the effective annual rate formula for compound interest, Scheme B yields 1.04 squared minus 1, which is an 8.16 percent return, and Scheme C yields 1.02 to the power of 4 minus 1, which is approximately an 8.24 percent return. Scheme A offers a fixed 9 percent annual return, which is higher than both 8.16 percent and 8.24 percent. Because 9 percent is the highest return, Scheme A yields the highest return on the investment.

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