Question

If the rate of interest is 8% per annum and Rs. 10000 lent at the compound interest half yearly then calculate the
equivalent simple rate of interest for the first year?
A. 8.16%
B. 9%
C. 7%
D. 10%​

Answer 1

Answer:

The correct option is A. 8.16%

Step-by-step explanation:

Let r be the equivalent rate of interest,

Since, the simple interest calculated annually,

$I=\frac{P\times r\times t}{100}$

While, the compound interest calculated semiannually,

$I=P-P(1+\frac{r}{200})^{2t}$

Where,

P = principal amount,

r = annual interest,

t = number of years,

Here,

$\frac{P\times r\times t}{100}=P(1+\frac{r}{200})^{2t}-P$

$\frac{rt}{100}=(1+\frac{r}{200})^{2t}-1$

If t = 1 year,

$\frac{r}{100}=(1+\frac{r}{200})^{2}-1$

If compound interest rate is 8%,

$\frac{r}{100}=(1+\frac{8}{200})^2-1$

$\frac{r}{100}=(1+\frac{1}{25})^2-1$

$0.01r = (\frac{26}{25})^2-1$

$0.01r =(1.04)^2-1$

$0.01r =1.0816-1$

$0.01r = 0.0816$

$\implies r =\frac{0.0816}{0.01}=8.16\%$

Hence, OPTION A is correct.

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