Answer:
The total interest earned on a $1,000 account over 8 years at a 3% interest rate, compounded semi-annually, is $269.74 to the nearest cent.
Step-by-step explanation:
To calculate how much interest an account earns for $1,000 over 8 years at 3%, compounded semi-annually, we use the formula for compound interest: A = P(1 + \frac{r}{n})^{nt}. In this formula, A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Given the problem:
P = $1,000
r = 3% or 0.03 (as a decimal)
n = 2 (since interest is compounded semi-annually)
t = 8 years
Plug these values into the formula:
A = $1,000(1 + \frac{0.03}{2})^{2\times8}
A = $1,000(1 + 0.015)^{16}
A = $1,000(1.015)^{16}
A = $1,000(1.26973856)
A = $1,269.74
The interest earned is therefore A - P = $1,269.74 - $1,000 = $269.74. This is the total interest earned over 8 years, to the nearest cent.