CAT 2023 Slot 1 QA Question & Solution
Question
Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is
Solution
Anil invested 22000 for 6 years at 4% interest compounded half-yearly
=> Amount =$22000\left(1.02\right)^{12}$
Let Sunil invest 'S' rupees for 5 years at 4% C.I. half-yearly and 10% S.I. for 1 additional year
=> Amount = $S\left(1.02\right)^{10}\left(1.1\right)$
Given that the both amounts are equal
=> $22000\left(1.02\right)^{12}=S\left(1.02\right)^{10}\left(1.1\right)$
=> $S=\dfrac{22000\left(1.02\right)^2}{1.1}=20808$