Questions: Find the value of the following ordinary annuity if interest is compounded annually. Find the total amount of interest earned. R=900, i=0.06, n=32 The value of the annuity is . (Round to the nearest cent as needed.)

Find the value of the following ordinary annuity if interest is compounded annually. Find the total amount of interest earned. R=900, i=0.06, n=32 The value of the annuity is . (Round to the nearest cent as needed.)
Transcript text: Find the value of the following ordinary annuity if interest is compounded annually. Find the total amount of interest earned. \[ \mathrm{R}=\$ 900, \mathrm{i}=0.06, \mathrm{n}=32 \] The value of the annuity is $\$$ $\square$ . (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Future Value of the Annuity

To find the future value \( FV \) of the ordinary annuity, we use the formula: \[ FV = R \times \frac{(1 + i)^n - 1}{i} \] Substituting the given values \( R = 900 \), \( i = 0.06 \), and \( n = 32 \): \[ FV = 900 \times \frac{(1 + 0.06)^{32} - 1}{0.06} \]

Step 2: Calculate Total Payments Made

The total payments made over the \( n \) periods can be calculated as: \[ \text{Total Payments} = R \times n \] Substituting the values: \[ \text{Total Payments} = 900 \times 32 \]

Step 3: Calculate Total Interest Earned

The total interest earned can be found by subtracting the total payments from the future value: \[ \text{Total Interest} = FV - \text{Total Payments} \] Using the values calculated in the previous steps, we find: \[ \text{Total Interest} = FV - (900 \times 32) \]

Final Answer

The value of the annuity is \(\boxed{104,195.73}\).

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