Final answer:
After 4 years with an annual interest rate of 2% compounded daily, an initial deposit of $1000 will grow to approximately $1083.86.
Step-by-step explanation:
To calculate how much money you will have in an account after 4 years with an initial deposit of $1000 and an annual interest rate of 2% compounded daily, you can use the formula for compound interest:
A = P(1 + \frac{r}{n})^{nt}
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
For your account:
P = $1000
r = 0.02 (2% annual interest)
n = 365 (compounded daily)
t = 4 years
Using the formula:
A = 1000(1 + \frac{0.02}{365})^{365*4}
Calculating this, we find:
A ≈ $1000(1.00005479452)^{1460}
A ≈ $1000(1.083859)
A ≈ $1083.86
Therefore, after 4 years, you will have approximately $1083.86 in your account.