On a certain principal if the Simple interest for two years is Rs 3000 and Compound interest for the two years is Rs 3225, what is the rate of Interest?
On a certain principal if the Simple interest for two years is Rs 3000 and Compound interest for the two years is Rs 3225, what is the rate of Interest?
1). 7.5 percent
2). 30 percent
3). 15 percent
4). 22.5 percent
2 answers
Formulas :- Simple Interest = ( Principal * Rate * Time ) / 100 Compound Interest = Principal [(1 + Rate / 100)^Time ] - Principal
Given :- Simple Interest = 3000 Compound Interest = 3225
Applying formula of Simple Interest Simple Interest = ( Principal * Rate * Time ) / 100 3000
= ( P * R * 2 ) / 100 (3000 * 100) / 2
= P * R (cross multiplication) 1500 * 100 = P * R ------------------------------------------------------------------------------Equation (1)
Applying formula of Compound Interest Compound Interest = Principal [(1 + Rate / 100)^Time ] - Principal
3225 = P [(1 + R/100)^2] - P using algebraic identity (a + b)^2 = a^2 + b^2 + 2 * a * b 3225 = P [(1 + R^2/ 100^2 + 2 * 1 * R/100)] - P 3225 = (P + (P*R^2/ 100^2 )+ 2 * P * R /100 ) - P 3225 = [100^2 * P + P * R^2 + P* R * 100 - 100^2 * P ] / 100^2 (Taking LCM) 3225 * 100 * 100 = P * R * R 2 + 200 * P * R or P * R ^2 + 200 * P * R using equation (1) putting value of PR 3225 * 100 * 100 = 1500 * 100 R + 200 * 1500 * 100 3225 * 100 * 100 = 15 * 100 * 100 R + 200 * 15 * 100 * 100 3225 * 100 * 100 - 200 * 15 * 100 * 100 = 15 * 100 * 100 R 3225 * 100 * 100 - 200 * 15 * 100 * 100 = 15 * 100 * 100 R 225 * 100 * 100 = 15 * 100 * 100 R 225 / 15 = R 15 = Rate of Interest