Ayaan invests a sum of money for 3 years compounded annually. He finds that the CI for the second year is ₹1260 and ₹1323 is the CI for the third year. Calculate the rate of interest and the sum invested by him.
Answers
Answer:
Dear student,
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
Thus, the rate of interest and actual sum of money are 5% per annum and Rs 24000 respectively.
Answer:
Answer is principal is 24000 rupees
Step-by-step explanation:
Rate of interest is 5 %p.a