At a certain rate per annum, the simple interest on a sum of money for one year is Rs. 260 and the compound interest on the same sum for two years is Rs.540.80. The rate of interest per annum is
)t ; CI = A - P Where, CI = Compound interest SI = Simple interest A = Amount on compound interest P = Principal R = rate % t = time in years Given, rate is same for calculating both SI and CI Let the rate be ‘R’. SI is calculated for 1 year SI = (P × R × 1)/100 = PR/100 Given, SI = Rs. 260 ⇒ PR/100 = 260 -------------eq (1) CI is calculated for 2 year ∴ A = P (1+
R
100
)2 As, CI = A – P ⇒ C. I = P ((1+
R
100
)2−1) Given, CI = Rs. 540.80 ∴ P((1+
R
100
)2−1)=540.80-----------eq (2) Dividing eq 2 by eq 1
P((1+
R
100
)2−1)
PR
100
=
540.80
260
⇒
((1+
R
100
)2−1)
R
100
=2.08 Using a2−b2=(a+b)(a−b) ⇒
(1+
R
100
+1)(1+
R
100
−1)
R
100
=2.08 ⇒ 2 + R/100 = 2.08 ⇒ R = 0.08 × 100 = 8% Smart Method Total SI for 1st and 2nd year = 260 + 260 = 520 Extra interest for 2nd year = 540.8 - 520 = 20.8 This extra interest is due to interest in 1st year SI. Hence, 260 × (R/100) = 20.8 ⇒ R = (208/10) × (100/260) ⇒ R = 8%