Question : If the 10 percent per annum rate of compound interest compounded yearly is equivalent to the x percent per annum rate of compound interest compounded half yearly, then what is the value (Approximate) of x?
Option 1: 6.25 percent
Option 2: 5.32 percent
Option 3: 4.88 percent
Option 4: 4.55 percent
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Correct Answer: 4.88 percent
Solution :
Annual interest rate = 10%
Compounding frequency = half-yearly
If x% is compounded half-yearly. Then, By using effective rate = a + b +$\frac{\text{ab}}{100}$,
⇒ Effective rate of interest = x + x + $\frac{\text{x}^2}{100}$
⇒ Effective rate of interest = 2x + $\frac{\text{x}^2}{100}$
According to the question:
⇒ 10 = 2x + $\frac{\text{x}^2}{100}$
⇒ 1000 = x(200 + x) ---(1)
It is better to use the option method after this. Just put values from options in equation (1).
x = 4.88 percent
Hence, the correct answer is 4.88 percent.
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