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Examples 1 to 4

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(1) Find compound interest on Rs. 50000 at 10 % per annum for 2 years.

Soln.

C.I. = P $\left [\left (1+\frac{R}{100} \right )^{N}-1 \right ]$

= 50000 $\left [\left (\frac{110}{100}\times \frac{110}{100} \right )-1 \right ]$ = Rs. 10500

(2) Find compound interest on Rs. 10000 at 18 % per annum for 1 year, compounded half-yearly.

Soln. Here, K = 2 $\large \Rightarrow$ No. of years = N = 2 $\times$ 1 = 2

A = 10000 $\times \frac{218}{200} \times \frac{218}{200}$ $\left (\because K=2 \Rightarrow use \frac{200+R}{200} \right )$

= Rs. 11881

C. I. = A – P = 11881 – 10000 = Rs. 1881

(3) Find compound interest on Rs. 8000 at 20 % per annum for 9 months, compounded quarterly.

Soln. Here, K = 4 $\large \Rightarrow$ No. of years = N $\times \frac{9}{12}$ = 4 = 3

A = 8000 $\times \frac{420}{400}\times \frac{420}{400}\times \frac{420}{400}$ $\left (\because K=4 \Rightarrow use \frac{400+R}{400} \right )$

= Rs. 9261

C.I. = A – P = 9261 – 8000 = Rs. 1261

(4) Find the difference between the compound interest and the simple interest on a Rs. 20,000 at 20 % per annum for 2 years.

Soln. Here, N = 2 yrs., P = 20000, R = 20

C.I. – S. I. = $\frac{PR ^{2}}{\left (100 \right )^{2}}$

= $\frac{2000 \times \left (20 \right )^{2}}{\left (100 \right )^{2}}$ = Rs. 800