You invest $1,000 at 4% compounded daily. Two years later you take the balance and place it into an account earning 4.5% compounded daily. Determine the value of your account three years after the 2nd investment.

P1 = Po(1+r)^n.

r = 0.04/365 = 0.0001096/day.
n = 365Comp./yr. * 2yrs. = 730 Compounding periods.
P1 = 1000(1.0001096)^730 = $1083.28.

P2 = Po(1+r)^n.
Po = P1 = 1083.28.
r = 0.045/365 = 0.0001233.
n = 365Comp./yr. * 3yrs = 1095 Compounding periods.
P2 = Value after 3 yrs. = ?.

To determine the value of your account three years after the second investment, we need to calculate the balances at each stage. Let's break it down step by step:

Step 1: Calculate the balance after the first investment period of two years.
To calculate the balance after two years with daily compounding at 4%, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the balance after the investment period
P = the initial principal amount ($1,000)
r = the annual interest rate (4% or 0.04)
n = the number of times interest is compounded per year (365, since it's compounded daily)
t = the number of years (2 years)

Plugging in the values, we get:

A = $1,000(1 + 0.04/365)^(365*2)
A ≈ $1,083.39

So, after the first investment period of two years, the balance in your account is approximately $1,083.39.

Step 2: Calculate the balance after the second investment period of one year.
Now, take the balance of $1,083.39 and calculate the balance after one more year with daily compounding at 4.5%. We'll use the same compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the balance after the investment period
P = the initial principal amount ($1,083.39)
r = the annual interest rate (4.5% or 0.045)
n = the number of times interest is compounded per year (365, since it's compounded daily)
t = the number of years (1 year)

Plugging in the values, we get:

A = $1,083.39(1 + 0.045/365)^(365*1)
A ≈ $1,133.85

So, after the second investment period of one year, the balance in your account is approximately $1,133.85.

Therefore, the value of your account three years after the second investment is approximately $1,133.85.