Questions: Find the compound interest and future value. Do not round intermediate steps. Round your answers to the nearest cent. Principal 835, Rate 5%, Time Annually, 8 years The future value is s, and the compound interest is s.

Solution Steps

Let \( P = 835 \) (the principal), \( r = 0.05 \) (the annual interest rate), \( n = 1 \) (the number of times interest is compounded per year), and \( t = 8 \) (the time in years).

Using the formula for compound interest, we calculate the future value \( A \) as follows:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the values:

\[ A = 835 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 8} \]

This simplifies to:

\[ A = 835 \left(1 + 0.05\right)^{8} = 835 \left(1.05\right)^{8} \]

The compound interest \( CI \) is found by subtracting the principal from the future value:

\[ CI = A - P \]

Substituting the values:

\[ CI = 1233.68 - 835 \]

Finally, round the future value and compound interest to the nearest cent:

\[ \text{Future Value} = 1233.68 \] \[ \text{Compound Interest} = 398.68 \]

Final Answer