Final answer:
To find how long it takes for an investment to double at a 3% interest rate compounded quarterly, use the compound interest formula. By plugging in the appropriate values, the time it takes is approximately 9.42 years.
Step-by-step explanation:
To find how long it takes for an investment to double at a 3% interest rate compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(nt).
Here, A represents the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial principal is $1,100 and we want it to double, so the final amount (A) is $2,200.
The interest rate (r) is 3% or 0.03, the number of times the interest is compounded (n) is 4 (quarterly), and t is the unknown variable we want to solve for.
Plugging in the values into the formula:
2,200 = 1,100(1 + 0.03/4)^(4t).
Solving for t, we can take the logarithm of both sides and rearrange the equation to isolate t.
After calculations, we find that t is approximately 9.42 years.