Using the formula for compound interest, where:
A = final amount = 15100 dollars
P = principal = 9000 dollars
r = annual interest rate = 5.5%
n = number of times interest is compounded per year (usually monthly or quarterly, but not specified in the problem)
t = time in years
We have:
15100 = 9000(1 + 0.055/n)^(nt)
To solve for t, we need to use logarithms:
ln(15100/9000) = t ln(1 + 0.055/n)
t = ln(15100/9000) / ln(1 + 0.055/n)
Using a calculator, we get:
t ≈ 6.68 years
Therefore, the person must leave the money in the bank for approximately 6.68 years to reach 15100 dollars.