$1,000 is invested at 8% interest compound annually $80 and interest is earned in the first year knowing the compound interest grows exponentially how much interest is earned in the second year including dollar and cents so if one year you got 80 what are you going to get after 2 years

Answer 1

To calculate the amount of interest earned in the second year of a compound interest investment, you can start with the information provided.

You initially have an investment of $1,000 at an annual interest rate of 8%.

1. Calculate the amount at the end of the first year:

   \[ A_1 = P(1 + r) \] where:

   • \( P = 1000 \) (initial investment),
   • \( r = 0.08 \) (annual interest rate).

   \[ A_1 = 1000(1 + 0.08) = 1000 \times 1.08 = 1080 \]

   So, the amount after the first year is $1,080. The interest earned in the first year is:

   \[ \text{Interest}_1 = A_1 - P = 1080 - 1000 = 80 \]

2. Calculate the amount at the end of the second year:

   Now, we use the amount at the end of the first year as the principal for the second year:

   \[ A_2 = A_1(1 + r) = 1080(1 + 0.08) \]

   \[ A_2 = 1080 \times 1.08 = 1166.40 \]

3. Calculate the interest earned in the second year:

   To find the interest earned in the second year, subtract the amount at the end of the first year from the amount at the end of the second year:

   \[ \text{Interest}_2 = A_2 - A_1 = 1166.40 - 1080 = 86.40 \]

So, the interest earned in the second year is $86.40.