To calculate the total interest accrued on Kate's account at the end of 3 years with a principal amount of $5000 and an annual compounded interest rate of 8%, we will use the formula for compound interest:
\[ A = P(1 + r/n)^{nt} \]
where:
- \( A \) 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.
- \( t \) is the time the money is invested for, in years.
In Kate's case, the interest is compounded yearly, so \( n = 1 \). The interest rate is 8%, so \( r = 0.08 \), and the time is 3 years (\( t = 3 \)).
Let's plug the values into the formula:
\[ A = 5000(1 + 0.08/1)^{1*3} \]
\[ A = 5000(1 + 0.08)^3 \]
\[ A = 5000(1.08)^3 \]
Now we calculate \( (1.08)^3 \) and multiply that by the principal amount of $5000 to get the final amount.
So, after 3 years, the amount in Kate's account will be $6298.56.
To find the total interest earned, we subtract the principal from the final amount:
\[ \text{Total Interest} = A - P \]
\[ \text{Total Interest} = 6298.56 - 5000 \]
\[ \text{Total Interest} = 1298.56 \]
Therefore, the total interest in Kate's account at the end of 3 years is $1298.56.
