Questions: Find the amount of the following ordinary annuities rounded to the nearest cent. Find the total interest earned. Amount of each deposit Deposited Rate Time (Years) Amount of an Annuity Interest Earned ------------------ 700 semiannually 12% 12 Click the icon to view the Amount of an Annuity Table. The amount of the annuity is approximately (Round to the nearest cent as needed.)

Solution Steps

We are given:

• Amount of each deposit: \( P = \$700 \)
• Annual interest rate: \( r = 0.12 \)
• Time in years: \( t = 12 \)
• Compounding periods per year: \( m = 2 \) (semiannually)

The number of periods \( n \) and the interest rate per period \( i \) are calculated as follows: \[ n = t \times m = 12 \times 2 = 24 \] \[ i = \frac{r}{m} = \frac{0.12}{2} = 0.06 \]

The future value \( FV \) of an ordinary annuity is given by: \[ FV = P \times \left( \frac{(1 + i)^n - 1}{i} \right) \] Substituting the values: \[ FV = 700 \times \left( \frac{(1 + 0.06)^{24} - 1}{0.06} \right) \] \[ FV = 700 \times \left( \frac{(1.06)^{24} - 1}{0.06} \right) \] \[ FV \approx 700 \times 50.8156 = 35570.9 \]

The total amount deposited \( D \) and the interest earned \( I \) are calculated as follows: \[ D = P \times n = 700 \times 24 = 16800 \] \[ I = FV - D = 35570.9 - 16800 = 18770.9 \]

Final Answer