Suppose you deposit $1500 into an account that pays 7% annual interest, compounded daily. To find the balance after 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where A is the balance, P is the principal (the initial deposit), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $1500, r = 0.07, n = 365, and t = 2. Substituting these values into the formula, we get:
A = 1500(1 + 0.07/365)^(365*2)
A = 1500(1.00019196)^730
A = 1500(1.15229558)
A = $1728.44
Therefore, the balance after 2 years with daily compounding is $1728.44, rounded to the nearest cent. This means that your initial deposit of $1500 has earned you $228.44 in interest over the course of 2 years.