Questions: Use the appropriate formula for an annuity and the given variables to solve for the missing variable. Round to the nearest hundredth or cent. Payments are made at the end of the compounding period. R=60, r=1%, m=1, n=240

Solution Steps

To solve for the future value of an annuity where payments are made at the end of each compounding period, we can use the future value of an ordinary annuity formula:

\[ FV = R \times \frac{(1 + r/m)^{mn} - 1}{r/m} \]

where:

• \( R \) is the regular payment amount,
• \( r \) is the annual interest rate (as a decimal),
• \( m \) is the number of compounding periods per year,
• \( n \) is the number of years.

Given the values \( R = 60 \), \( r = 0.01 \), \( m = 1 \), and \( n = 240 \), we can substitute these into the formula to find the future value.

We are given the following variables for the annuity calculation:

• \( R = 60 \) (the regular payment amount)
• \( r = 0.01 \) (the annual interest rate)
• \( m = 1 \) (the number of compounding periods per year)
• \( n = 240 \) (the total number of payments)

We will use the future value of an ordinary annuity formula:

\[ FV = R \times \frac{(1 + \frac{r}{m})^{mn} - 1}{\frac{r}{m}} \]

Substituting the given values into the formula:

\[ FV = 60 \times \frac{(1 + \frac{0.01}{1})^{1 \times 240} - 1}{\frac{0.01}{1}} \]

Calculating the expression step-by-step:

1. Calculate \( 1 + \frac{0.01}{1} = 1.01 \).
2. Raise \( 1.01 \) to the power of \( 240 \): \[ (1.01)^{240} \approx 6.223 \]
3. Subtract \( 1 \): \[ 6.223 - 1 = 5.223 \]
4. Divide by \( \frac{0.01}{1} = 0.01 \): \[ \frac{5.223}{0.01} = 522.3 \]
5. Finally, multiply by \( 60 \): \[ FV = 60 \times 522.3 = 31338 \]

Final Answer