Question

the difference between the CI  and SI on a certain sum of money at the rate of 10 % per annum for 2 years Rs 200.find the sum when the interest is compounded annually

Answer 1

rate = 10%
time = 2 years
n = 1 (as compounded annually )
Let the principal = P

$SI = \frac{Ptr}{100} = \frac{P*2*10}{100}=0.2P$

$CI = P[(1+ \frac{r}{n})^ {nt}-1\ ]=P[(1+ 0.1)^ {2}-1\ ]=P[1.21-1]=0.21P$

Given that 0.21P -  0.2P = 200
⇒ 0.01 P = 200
⇒P = 200/0.01
⇒P = 20000

Compound Interest = 0.21P = 0.21×20000 = Rs. 4200
Total amount = 20000+4200 = Rs. 24200