Questions: Find the future value for the annuity due with the given rate. Payments of 14,000 for 13 years at 0.21% compounded monthly The future value of the annuity due is

Solution Steps

To find the future value of an annuity due, we need to use the formula for the future value of an annuity due, which is:

\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r) \]

where:

• \( P \) is the payment amount per period
• \( r \) is the interest rate per period
• \( n \) is the total number of payments

Given:

• Payments (\( P \)) = \$14,000
• Number of years = 13
• Annual interest rate = 0.21%
• Compounded monthly

First, we need to convert the annual interest rate to a monthly interest rate and calculate the total number of payments.

We are given the following values for the annuity due:

• Payment amount per period, \( P = 14000 \)
• Annual interest rate, \( r = 0.0021 \)
• Number of years, \( t = 13 \)

The monthly interest rate is calculated as: \[ r_{monthly} = \frac{r}{12} = \frac{0.0021}{12} = 0.000175 \]

The total number of payments over 13 years, compounded monthly, is: \[ n = t \times 12 = 13 \times 12 = 156 \]

Using the formula for the future value of an annuity due: \[ FV = P \times \left( \frac{(1 + r_{monthly})^n - 1}{r_{monthly}} \right) \times (1 + r_{monthly}) \] Substituting the values: \[ FV = 14000 \times \left( \frac{(1 + 0.000175)^{156} - 1}{0.000175} \right) \times (1 + 0.000175) \] Calculating this gives: \[ FV \approx 2214275.8119552694 \]

Rounding the future value to the nearest dollar: \[ FV_{rounded} = 2214276 \]

Final Answer