Question

A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years is Rs. 650 and Rs. 760.50; Find the rate of interest.
(a) 34
(b) 32
(c) 27
(d) 38

Answer 1

Hint: First, we have to find the difference between the compound interest (CI) of two successive years. Then we will use the formula difference between two successive years $=\dfrac{PRN}{100}$ . Here, N is number of period which is $\dfrac{1}{2}year$ , R is rate of interest which we have to find, P is principal amount which will be of preceding year i.e. Rs, 650. Thus, on solving we will get our answer.
Complete step-by-step answer:
Here, we are given interest for two successive half-years i.e. $\dfrac{1}{2}year$ as Rs. 650 and Rs. 760.50.
So, we will find the difference between the compound interest (CI) of two successive years as
$=760.50-650=Rs.110.50$
Now, we will use the formula as difference between two successive years $=\dfrac{PRN}{100}$
Here, R is rate of interest which we have to find, N is tie period which is $\dfrac{1}{2}year$ , is principal amount of preceding year i.e. Rs. 650.
So, on substituting the values we will get
$110.50=\dfrac{650\times R\times \dfrac{1}{2}}{100}$
On making R as subject variable, we will get equation as
$R=\dfrac{110.50\times 100\times 2}{650\times 1}$
$R=34\%$
Thus, we get a rate of interest as 34%.
Hence, option (a) is the correct answer.

Note: Be careful while taking principal value out of Rs. 650 and Rs. 760.50. It should always be preceding value. Students make the mistake while taking principal amount as Rs. 760.50 So, it leads to the wrong answer. By this, we will get an answer as $R=\dfrac{110.50\times 100\times 2}{750.50\times 1}$ . On solving, we will get $R=29.44\%$ which is incorrect. So, be careful while considering the principal amount to avoid making mistakes.