$2,000 principal earning 3%, compounded annually, after 3 years.
P = Po(1+r)^n.
n = 1comp./yr * 3yrs = 3 Compounding periods.
P = 2000(1+.03)^3 = $2,185.45.
To calculate the compound interest earned on a principal amount, you can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A is the final amount (including both the principal and the interest),
P is the principal amount,
r is the annual interest rate (expressed as a decimal),
n is the number of times interest is compounded per year,
t is the number of years.
In this case, you have a principal (P) of $2,000, an interest rate (r) of 3% (or 0.03 as a decimal), and the interest is compounded annually (n = 1). The question asks for the value after 3 years (t = 3).
Plugging these values into the formula:
A = 2000(1 + 0.03/1)^(1*3)
= 2000(1 + 0.03)^3
= 2000(1 + 0.03)^3
= 2000(1.03)^3
= 2000(1.092727)
= $2,185.45
Therefore, the final amount after 3 years, with a $2,000 principal earning 3% compounded annually, would be approximately $2,185.45.