To calculate the interest earned in the second year when $1000 is invested at an 8% interest rate compounded annually, we start with the following information:
- Principal (P): $1000
- Interest Rate (r): 8% (or 0.08 in decimal form)
In the first year, the interest earned is calculated as follows:
\[ \text{Interest for Year 1} = P \times r = 1000 \times 0.08 = 80 \]
This confirms that $80 in interest is indeed earned in the first year.
To find the total amount after the first year, we add the interest earned to the principal:
\[ \text{Total Amount after Year 1} = P + \text{Interest for Year 1} = 1000 + 80 = 1080 \]
In the second year, the interest is calculated on the new principal, which is the amount after the first year:
\[ \text{Principal for Year 2} = 1080 \]
Now, we will calculate the interest earned in the second year using the same interest rate:
\[ \text{Interest for Year 2} = \text{Principal for Year 2} \times r = 1080 \times 0.08 \]
Calculating that gives:
\[ \text{Interest for Year 2} = 1080 \times 0.08 = 86.4 \]
Therefore, the amount of interest earned in the second year is:
\[ \text{Interest for Year 2} = 86.40 \]
So, the final answer is:
\[ \boxed{86.40} \]
1 answer