CAT Exam 2021 Slot 1 Solved Paper

Question : 56 of 66

Marks: +1, -0

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

929.48
934.65
931.72
926.84

Validate

Solution:

Let the principal amount be P and the interest rate be r.
Then

\P(1 + \r)^2 - \P(1 + \r)=806.25

...(1)

\P(1 +\r)^3 - \P(1 -\r)^2 = 866.72

...(2)

dividing (2) by (1) we get :

(\P ( 1 + \r_)^3 - \P(1+\r)^2 )/(\P(1+\r)^2 -\P(1+\r) )= 866.72/806.25

((1+\r)^2 -1 -\r) / (1+\r-1) = 1.075

{\r^2 +\r}/\r = 1.075

\r= 0.075

or 7.5%

{\interest \accrued \in \4\th \yr}/ {\interest \accrued \in \3\rd \yr } =\x/866.72

{\P(1+\r)^4 - \P(1+\r)^3}/ {\P(1+\r^)^3 - \P(1+\r)^2} = \x/866.72

Dividing numerator and denominator by

\P(1+\r)^2

{\r^2+2\r + 1-1-\r}/ {1+\r-1} = \x /866.72

\r+1 = \x/866.72

\x= 1.075×866.72= 931.72

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