If a sum of money doubles in 5 years at simple interest, what is the rate of interest per annum?
Practice Questions
1 question
Q1
If a sum of money doubles in 5 years at simple interest, what is the rate of interest per annum?
10%
20%
15%
25%
The formula for simple interest is A = P(1 + rt). If the amount doubles, A = 2P. Therefore, 2P = P(1 + r*5). Simplifying gives r = 0.1 or 10%.
Questions & Step-by-step Solutions
1 item
Q
Q: If a sum of money doubles in 5 years at simple interest, what is the rate of interest per annum?
Solution: The formula for simple interest is A = P(1 + rt). If the amount doubles, A = 2P. Therefore, 2P = P(1 + r*5). Simplifying gives r = 0.1 or 10%.
Steps: 9
Step 1: Understand that simple interest means the interest is calculated on the original amount of money (P).
Step 2: Know that if the sum of money doubles, the final amount (A) will be 2 times the original amount (A = 2P).
Step 3: Use the formula for simple interest: A = P(1 + rt), where A is the final amount, P is the principal amount, r is the rate of interest, and t is the time in years.
Step 4: Substitute A with 2P in the formula: 2P = P(1 + r*5).
Step 5: Divide both sides of the equation by P (assuming P is not zero): 2 = 1 + r*5.
Step 6: Subtract 1 from both sides: 2 - 1 = r*5, which simplifies to 1 = r*5.
Step 7: Divide both sides by 5 to solve for r: r = 1/5.
Step 8: Convert r into a percentage: r = 0.2 or 20%.
Step 9: Conclude that the rate of interest per annum is 20%.
