Final answer:
To calculate the time required for $5,000 to grow to $15,000 at a 6% interest rate compounded quarterly, the compound interest formula A = P(1 + r/n)^(nt) is used. By solving the equation with the given values, one can determine the time in years and then multiply by 4 to convert it to quarters.
Step-by-step explanation:
To determine how long it will take for $5,000 to grow to $15,000 with interest compounded quarterly at a rate of 6%, we use 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 (the initial sum of money), 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.
We are looking for the time, t, when the investment grows to $15,000. So, the equation to solve is $15,000 = $5,000(1 + 0.06/4)^(4t). To find t, we need to isolate it on one side of the equation, which typically involves using logarithms.
However, rather than solving it step by step, I can tell you that this type of equation can be rearranged and solved using logarithms, yielding the value of t in years, and then multiplying by 4 to find the number of quarters.