A certain sum of money is lent at a 10% annual compound interest rate, payable…
2023
A certain sum of money is lent at a 10% annual compound interest rate, payable half-yearly. What is the effective annual rate of interest?
- A.
10.10%
- B.
10.16%
- C.
10.20%
- D.
10.25%
Attempted by 8 students.
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Correct answer: D
To find the effective annual rate, first determine the periodic interest rate. Since the nominal rate is 10% compounded half-yearly, divide by 2 to get 5% per period.
Next, calculate the effective rate using the formula (1 + r)^n - 1, where r is the periodic rate and n is the number of periods per year. Here, (1 + 0.05)^2 - 1 = 1.1025 - 1 = 0.1025.
Convert the decimal to a percentage: 0.1025 × 100 = 10.25%.