Question

Simple interest on a sum of money for 2 years at 4% is ₹450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half yearly. [3 Mark]

Answer 1

Given: S.I. = ₹450; N = 2 years and rate(R) = 4%
Let’s consider the principal to be P
Now, we have
P = (S.I x 100)/(R x T)
= (450 x 100)/(4 x 2)
= 5625 [1 Mark]
Thus, the principal is ₹5625
Now,
When the interest is compounded half-yearly
P = ₹5,625; n = 1 year and r = 4%
A = P[1 + r/(2 x 100)]^(n x 2)
= 5625(1 + 4/200)^(1 x 2)
= 5625(51/50)^2
= 5852.25 [1.5 Mark]
Hence,
C.I. = ₹5852.25 – ₹5,625
= ₹227.25 [0.5 Mark]