A certain amount of money triples itself in 15 years at compound interest. What is the annual interest rate?
Practice Questions
1 question
Q1
A certain amount of money triples itself in 15 years at compound interest. What is the annual interest rate?
5%
6%
7%
8%
Using the formula A = P(1 + r)^n, we can set up the equation 3P = P(1 + r)^15. Solving for r gives approximately 6%.
Questions & Step-by-step Solutions
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Q
Q: A certain amount of money triples itself in 15 years at compound interest. What is the annual interest rate?
Solution: Using the formula A = P(1 + r)^n, we can set up the equation 3P = P(1 + r)^15. Solving for r gives approximately 6%.
Steps: 9
Step 1: Understand the problem. We want to find the annual interest rate (r) that makes a certain amount of money (P) triple in 15 years.
Step 2: Write down the formula for compound interest: A = P(1 + r)^n, where A is the amount of money after n years, P is the principal amount, r is the annual interest rate, and n is the number of years.
Step 3: Since the money triples, we can say A = 3P. So we can rewrite the formula as 3P = P(1 + r)^15.
Step 4: Divide both sides of the equation by P (assuming P is not zero): 3 = (1 + r)^15.
Step 5: To solve for r, we need to isolate (1 + r). Take the 15th root of both sides: 1 + r = 3^(1/15).
Step 6: Calculate 3^(1/15) using a calculator. This gives approximately 1.0794.
Step 7: Now, subtract 1 from both sides to find r: r = 1.0794 - 1 = 0.0794.
Step 8: Convert r into a percentage by multiplying by 100: r = 0.0794 * 100 = 7.94%.
Step 9: Round the answer to the nearest whole number, which gives us approximately 8%.
