If a sum of money triples itself in 15 years at simple interest, what is the rate of interest?
Practice Questions
1 question
Q1
If a sum of money triples itself in 15 years at simple interest, what is the rate of interest?
5%
6.67%
10%
15%
If the sum triples, the interest earned is 2P in 15 years. Thus, 2P = PRT implies R = 2/15 = 13.33%, which is approximately 6.67%.
Questions & Step-by-step Solutions
1 item
Q
Q: If a sum of money triples itself in 15 years at simple interest, what is the rate of interest?
Solution: If the sum triples, the interest earned is 2P in 15 years. Thus, 2P = PRT implies R = 2/15 = 13.33%, which is approximately 6.67%.
Steps: 10
Step 1: Understand that if a sum of money triples, it means the final amount is three times the original amount. If the original amount is P, then the final amount is 3P.
Step 2: In simple interest, the formula for the final amount is: Final Amount = Principal + Interest. Here, Interest = PRT, where P is the principal, R is the rate of interest, and T is the time in years.
Step 3: Since the final amount is 3P, we can write the equation: 3P = P + Interest.
Step 4: Rearranging the equation gives us: Interest = 3P - P = 2P.
Step 5: Now, we know that Interest = PRT. So, we can substitute: 2P = PRT.
Step 6: We can divide both sides of the equation by P (assuming P is not zero): 2 = RT.
Step 7: We know that T is 15 years, so we can substitute T into the equation: 2 = R * 15.
Step 8: To find R, divide both sides by 15: R = 2 / 15.
Step 9: Convert R into a percentage by multiplying by 100: R = (2 / 15) * 100.
Step 10: Calculate the percentage: R = 13.33%. Therefore, the rate of interest is approximately 6.67%.
