Final answer:
To triple an investment in 17 years, the required interest rate compounded annually is approximately 6.61%.
Step-by-step explanation:
The question is asking for the annual interest rate that when compounded yearly would triple an investment in 17 years. To calculate this, we use the formula for compound interest, which is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), and n is the number of years the money is invested. We set the future value A to be three times the principal P, and solve for r.
To find out the required interest rate, we set up the equation 3P = P(1 + r)^17 and solve for r:
- Divide both sides by P to get 3 = (1 + r)^17
- Take the 17th root of both sides to get (1 + r) = 3^(1/17)
- Subtract 1 from both sides to get r = 3^(1/17) - 1
- Finally, convert r to a percentage by multiplying by 100
Doing the math, we find the correct interest rate to be approximately 6.61% compounded annually.