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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?
- A7.5 percent
- B30 percent
- C15 percent
- D22.5 percent
Answer not set
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0
CCommunity
I have read it somewhere 15 percent is correct
0
CCommunity
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
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