Final answer:
To quadruple an investment at 7% interest compounded weekly, it will take approximately 20.91 years, determined by using the compound interest formula and solving for the time variable.
Step-by-step explanation:
To calculate how long it will take for money to quadruple when invested at a 7% interest rate compounded weekly, we utilize the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Since we want the final amount to be four times the initial investment, we set A = 4P. With weekly compounding, n is 52, and the rate r is 0.07 (since 7% = 0.07). The formula becomes: 4P = P(1 + 0.07/52)^(52t).
To solve for t, we first divide both sides by P and then simplify as follows:
- 4 = (1 + 0.07/52)^(52t)
- ln(4) = ln((1 + 0.07/52)^(52t))
- ln(4) = 52t * ln(1 + 0.07/52)
- t = ln(4) / (52 * ln(1 + 0.07/52))
Using a calculator to compute this gives us t ≈ 20.91 years. Therefore, to quadruple your investment at 7% interest compounded weekly, it will take approximately 20.91 years.