Questions: Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. R=900; 6.04% interest compounded semiannually for 9 years. The future value of the ordinary annuity is . (Round to the nearest cent as needed.)

Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
R=900; 6.04% interest compounded semiannually for 9 years.

The future value of the ordinary annuity is .
(Round to the nearest cent as needed.)

Transcript text: Find the future value of an ordinary annuity if payments are made in the amount $R$ and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. $R=900 ; 6.04 \%$ interest compounded semiannually for 9 years. The future value of the ordinary annuity is $\$$ $\square$ (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Calculate the future value (FV) of the annuity

Using the formula $FV = R \times \frac{(1 + i)^n - 1}{i}$, where $R = 900$, $i = 0.0302$, and $n = 18$, we find $FV = 900 \times \frac{(1 + 0.0302)^18 - 1}{0.0302} = 21111.05.$

Step 2: Determine the total contributions

The total contributions are calculated as $R \times n = 900 \times 18 = 16200.$

Step 3: Calculate the portion of the future value that comes from interest

The portion from interest is $FV - R \times n = 21111.05 - 16200 = 4911.05.$