Question

The compouned interest, calculate yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money

• A. 11%, Rs. 800
• B. 12%, Rs. 400
• C. 13%, Rs. 700
• D. None of these
  

Answer 1

Answer: (D)

None of these

Sum after 2 years=Rs.1089

Sum after 3 years=Rs.1197.90

Interest for onr year$=1197.90-1089=108.90$

C.I for 1 year=S.I for 1 year

$Interest=\frac{PRT}{100}$

$\Rightarrow 108.90=\frac{1089\times R\times 1}{100}$

$\Rightarrow R=\frac{108.90\times 100}{1089}=10$%

Let the sum=Rs.x

Amount=Rs. 1089,Time 2 years,R=10%

$Amount=P{(1+\frac{R}{100})}^t$

$\Rightarrow 1089=x{(1+\frac{10}{100})}^2$

$\Rightarrow 1089=x\times \frac{110}{100}\times \frac{110}{100}$

$\Rightarrow x=\frac{1089\times 100\times 100}{110\times 110}=Rs.900$