​ A sum of Rs 24000 is borrowed for 1(1/2)years at the rate of interest 10% per annum compounded semi anually. ​

Question

A sum of Rs 24000 is borrowed for \(1\frac{1}{2}\) years at the rate of interest 10% per annum compounded semi anually. What is the compound interest (x) ?

(a) x < Rs 3000

(b) Rs 3000 < x < Rs 4000

(c) Rs 4000 < x < Rs 5000

(d) x > Rs 5000

Answer 1

(b) Rs 3000 < x < Rs 4000

P = Rs 24000, Time =\(1\frac{1}{2}\) years = 3 half years,

r = 10% p.a. = 5% per half year

\(\therefore\) A = 24000\(\big(1+\frac{5}{100}\big)^3\) = 24000 x \(\big(\frac{21}{20}\big)^3\)

= 24000 x \(\frac{9261}{8000}\) = Rs 27783.

\(\therefore\) C.I. = Rs 27783 – Rs 24000 = Rs 3783

\(\therefore\) C.I. (x) lies between Rs 3000 and Rs 4000.