Final answer:
To find the time required for money to quadruple at a simple interest rate of 15%, the simple interest formula is modified to solve for time. At a rate of 15%, it takes 20 years for the initial investment to reach four times its original value.
Step-by-step explanation:
To calculate the length of time required for money to quadruple in value at a simple interest rate of 15% per year, we can utilize the formula for simple interest and set up an equation to find the number of years needed. The simple interest formula is I = P × r × t, where I is the interest earned, P is the principal amount, r is the interest rate, and t is the time in years.
To quadruple the money, the future value needs to be four times the principal, so we set 4P = P + I (where I is the interest). Since I = P × 0.15 × t, we substitute to get 4P = P + (P × 0.15 × t). After simplifying, this leads to 3P = P × 0.15 × t, and then t = 3 / 0.15, which equals 20 years.
Therefore, at a simple interest rate of 15% per annum, it would take 20 years for the money to quadruple in value.