Final answer:
To find the time it takes for your investment to double, you can use the formula for compound interest. In this case, it will take approximately 34.85 years for your money to double if it is invested in a bank earning 2% interest compounded quarterly.
Step-by-step explanation:
To find the time it takes for your investment to double, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, 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, P = $200 and we want to find t. We know that A = 2P, so we can plug in the values into the formula:
2P = P(1+0.02/4)^(4t)
Divide both sides by P:
2 = (1+0.02/4)^(4t)
Take the logarithm of both sides:
log(2) = log((1+0.02/4)^(4t))
Use the power rule of logarithms:
log(2) = 4t * log(1+0.02/4)
Divide both sides by 4 * log(1+0.02/4):
t = log(2) / (4 * log(1+0.02/4))
Using a calculator, we can find that t ≈ 34.85 years.