To find the amount of interest earned in the second year on an investment of $1000 at 8% interest compounded annually, we start by determining the amount at the end of the first year.
The formula for compound interest is:
\[ A = P(1 + r)^t \]
where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial investment).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time in years.
For the first year (where \(t = 1\)):
- \(P = 1000\)
- \(r = 0.08\)
Calculating the amount after the first year:
\[ A = 1000(1 + 0.08)^1 = 1000(1.08) = 1080 \]
The interest earned in the first year is:
\[ \text{Interest} = A - P = 1080 - 1000 = 80 \]
The principal at the beginning of the second year is now \(1080\). We can calculate the interest earned in the second year using the same interest rate.
For the second year (where \(t = 1\) again, but now with a new principal):
\[ A = 1080(1 + 0.08)^1 = 1080(1.08) = 1166.40 \]
Now, we will calculate the interest earned in the second year:
\[ \text{Interest in second year} = A - \text{Principal at beginning of second year} = 1166.40 - 1080 = 86.40 \]
Thus, the interest earned in the second year is:
\[ \boxed{86.40} \]
1 answer