To find the annual payment of an annuity over 10 years where the total amount is $8000 and the interest rate is 4% compounded annually, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
Where:
- \( FV \) is the future value of the annuity (in this case, $8000)
- \( P \) is the annual payment
- \( r \) is the annual interest rate (as a decimal, so 4% = 0.04)
- \( n \) is the number of years (10 years)
We need to solve for \( P \). Rearranging the formula gives us:
\[ P = \frac{FV \times r}{(1 + r)^n - 1} \]
Now, substituting the known values into the equation:
\[ FV = 8000, \quad r = 0.04, \quad n = 10 \]
Calculating \( (1 + r)^n \):
\[ (1 + 0.04)^{10} = 1.04^{10} \approx 1.48024 \]
Now, plug this back into the formula:
\[ P = \frac{8000 \times 0.04}{1.48024 - 1} \] \[ P = \frac{320}{0.48024} \] \[ P \approx 666.45 \]
Thus, the size of the annual payment is approximately $666.45.