We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (6700 dollars)
P = the principal amount (5500 dollars)
r = the annual interest rate (4.5% or 0.045)
n = the number of times the interest is compounded per year (once annually)
t = the time period (in years) for which the money is invested
Substituting these values in the formula, we get:
6700 = 5500(1 + 0.045/1)^(1t)
Dividing both sides by 5500, we get:
1.21818181818 = 1.045^t
Taking the logarithm (base 10) of both sides, we get:
t = log(1.21818181818) / log(1.045)
Solving this equation using a calculator, we get:
t ≈ 4.4
Therefore, the person must leave the money in the bank for approximately 4.4 years (to the nearest tenth of a year) until it reaches 6700 dollars.