Short Answer 
The compound interest formula A = P (1 + r/n)^(nt) is used to calculate the total amount accumulated after interest. By plugging in an initial principal of $1000, an annual interest rate of 6%, compounded daily for 2 years, the final amount calculated is approximately $1182.43.
Step 1: Understand the Compound Interest Formula
To solve for the accumulated amount using the compound interest formula, familiarize yourself with the variables involved. The formula is represented as A = P (1 + r/n)^(nt), where:
- A: the total amount after interest
- P: the initial principal amount
- r: the annual interest rate in decimal
- n: the number of times interest is compounded per year
- t: the number of years the money is invested
Step 2: Plug in the Values
Now that you know the formula, insert the specific values from the problem into it:
- P = $1000
- r = 6% or 0.06
- n = 365 (compounding daily)
- t = 2 years
This gives you the expression: A = 1000 (1 + 0.06/365)^(365√ó2).
Step 3: Calculate the Final Amount
Perform the calculations step by step:
- Calculate the term inside the parentheses: 1 + (0.06/365) ≈ 1.0001643836
- Raise the result to the power of (365√ó2), which is 730.
- Multiply this value by the principal: A = 1000 √ó (1.0001643836)^730.
The final calculation yields A ≈ $1182.43, which represents the total amount accumulated after 2 years.