Question

Raju invested a sum of the amount in a bank at 10% interest rate. For the first three years, the interest calculated by the simple method. Then he switched to the compound interest plan in which the interest rate was one percentage point less than that of the simple interest plan. If the investment was for 5 years how much more interest amount he got because of the switching?
1. 6.3%
2. 7.2%
3. 8.9%
4. 10.1%

Answer 1

Correct Answer - Option 3 : 8.9%

Calculation:

Let P be the principal amount

The interest amount he would have received at simple interest plan = P × (r/100) × 5 = P × (10/100) × 5 = 0.5P

The interest amount after 3 years as per simple interest amount =  P × (r/100) × 3 = P × (10/100) × 3 = 0.3P

Switched to Compound interest plan after 3 years,

⇒ r_new = 9 %

⇒ P_new= P + 0.3 P 

⇒ t = 5 - 3 =2

⇒ Total amount = 1.3 × P × ( 1 + (9/100))² = 1.3 × P × 1.09² = 1.5445P

⇒ Extra amount because of switching = 1.5445P -1.5P = 0.0445P

⇒ In percentage = ((0.0445P)/(0.5P)) × 100 = 8.9 %

When the principal amount is not given, take the principal amount as P to find the answer. But in some cases, you can take the principal amount as 100, For example if the question is to find percentage or ratio and involves only one investment.