You deposit 5000 to an account that earns 5% compounded annually for two years and 7% in all subsequent years. What has the account grown to in 5 years?
To calculate the value of the account after 5 years, we'll need to consider the growth of the initial deposit over two periods: the first two years at 5% annual interest and the following three years at 7% annual interest.
For the first two years: [ A_2 = 5000 \times (1 + 0.05)^2 ] [ A_2 \approx 5512.50 ]
Now, let's calculate the growth from year 3 to year 5 at 7% annual interest: [ A_5 = A_2 \times (1 + 0.07)^3 ] [ A_5 = 5512.50 \times (1 + 0.07)^3 ]
Let's compute the final amount in the account after 5 years.
[ A_5 ≈ 5512.50 \times (1.07)^3 ] [ A_5 ≈ 5512.50 \times 1.1474875 ] [ A_5 ≈ 6306.19 ]
So, after 5 years, the account will have grown to approximately $6,306.19.
