Question

9. Ayaan invests a sum of money for 3 years compounded annually. He finds that CI for the second year is 21260
and 1323 is the Cl for the third year. Calculate the rate of interest and the sum invested by him.​

Answer 1

Answer:

Let the actual sum of money be Rs. P and the rate of interest be r% per annum

Compound Interest for the second year = Amount at the end of 2nd year – Amount at the end of 1st year

=P(1+r100)2−P(1+r100)

∴P(1+r100)2−P(1+r100)=1260

⇒P(1+r100)[(1+r100)−1]=1260 −−⎛⎝1⎞⎠Compound interest for the third year=P(1+r100)3−P(1+r100)2∴P(1+r100)3−P(1+r100)2=1323⇒P(1+r100)2[(1+r100)−1]=1323 −−⎛⎝2⎞⎠Dividing ⎛⎝2⎞⎠ by ⎛⎝1⎞⎠P(1+r100)2[(1+r100)−1]P(1+r100)[(1+r100)−1]=13231260⇒(1+r100)=13231260⇒r100=13231260−1⇒r100=1323−12601260⇒r100=631260⇒r=63001260⇒r=900180⇒r=5%Substituting r =5%, in equation ⎛⎝1⎞⎠, we get⇒P(1+5100)[(1+5100)−1]=1260 ⇒P(1+120)[1+120−1]=1260 ⇒P(2120)[120]=1260⇒P=1260×20×201×21⇒P=60×20×20⇒P=Rs 24000

Step-by-step explanation: