If a sum of money doubles itself in 5 years at simple interest, what will be the rate of interest per annum?
Practice Questions
1 question
Q1
If a sum of money doubles itself in 5 years at simple interest, what will be the rate of interest per annum?
10%
12%
15%
20%
Using the formula for simple interest, SI = PRT, where SI = Principal, R = Rate, and T = Time. If the principal doubles in 5 years, then SI = P. Therefore, P = PRT implies R = 1/5 = 20%. Hence, the rate of interest is 10%.
Questions & Step-by-step Solutions
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Q
Q: If a sum of money doubles itself in 5 years at simple interest, what will be the rate of interest per annum?
Solution: Using the formula for simple interest, SI = PRT, where SI = Principal, R = Rate, and T = Time. If the principal doubles in 5 years, then SI = P. Therefore, P = PRT implies R = 1/5 = 20%. Hence, the rate of interest is 10%.
Steps: 9
Step 1: Understand that the sum of money doubles in 5 years. This means if you start with an amount P, after 5 years, you will have 2P.
Step 2: Recall the formula for simple interest: SI = PRT, where SI is the simple interest, P is the principal amount, R is the rate of interest per annum, and T is the time in years.
Step 3: Since the money doubles, the simple interest (SI) earned in 5 years is equal to the principal amount (P). So, SI = P.
Step 4: Substitute SI in the formula: P = PRT. Here, SI is equal to P, so we have P = PRT.
Step 5: Divide both sides of the equation by P (assuming P is not zero): 1 = RT.
Step 6: Since the time T is 5 years, we can rewrite the equation as 1 = R * 5.
Step 7: To find R, divide both sides by 5: R = 1/5.
Step 8: Convert R into a percentage by multiplying by 100: R = (1/5) * 100 = 20%.
Step 9: Therefore, the rate of interest per annum is 20%.
