1. How long does it take a capital of $1,080,000 placed at 10% annually to reach another capital of $1,300,000 placed at 0.5% monthly? Consider simple interest.

1. Use the formula for simple interest to find the amount of each investment after time \(t\):

A_1 = 1080000(1 + 0.10t)

A_2 = 1300000(1 + 0.005 \times 12t)

2. Set the amounts of the two investments equal to each other:

1080000(1 + 0.10t) = 1300000(1 + 0.005 \times 12t)

3. Simplify and solve for \(t\):

1080000 + 1080000 \times 0.10 t = 1300000 + 1300000 \times 0.005 \times 12 t

1080000 + 108000 \, t = 1300000 + 78000 \, t

108000\,t-78000\,t=1300000-1080000

30000\,t=220000

t=\frac{220000}{30000}=\frac{22}{3}\approx7\text{ years and 4 months}

Answer: 7 years and 4 months