QuestionJuly 29, 2025

Find the value of an annuity at the end of a year in which you deposit 100 dollars per month at 12% compounded monthly.

Find the value of an annuity at the end of a year in which you deposit 100 dollars per month at 12% compounded monthly.
Find the value of an annuity at the end of a year in which you deposit 100 dollars per month
at 12%  compounded monthly.

Solution
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Answer

1268.25 Explanation 1. Identify the formula for future value of an annuity The future value of an annuity is calculated using **FV = P \times \frac{(1 + r)^n - 1}{r}**, where P is the monthly deposit, r is the monthly interest rate, and n is the total number of deposits. 2. Calculate monthly interest rate Convert annual interest rate to monthly: r = \frac{12\%}{12} = 0.01. 3. Determine the number of deposits Since deposits are made monthly for a year, n = 12. 4. Calculate the future value Substitute values into the formula: FV = 100 \times \frac{(1 + 0.01)^{12} - 1}{0.01}.

Explanation

1. Identify the formula for future value of an annuity<br /> The future value of an annuity is calculated using **$FV = P \times \frac{(1 + r)^n - 1}{r}$**, where $P$ is the monthly deposit, $r$ is the monthly interest rate, and $n$ is the total number of deposits.<br />2. Calculate monthly interest rate<br /> Convert annual interest rate to monthly: $r = \frac{12\%}{12} = 0.01$.<br />3. Determine the number of deposits<br /> Since deposits are made monthly for a year, $n = 12$.<br />4. Calculate the future value<br /> Substitute values into the formula: $FV = 100 \times \frac{(1 + 0.01)^{12} - 1}{0.01}$.
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