Answer:
approximately $232,969.76.
Explanation:
To calculate the future value of an ordinary annuity, you can use the formula:
Future Value = PMT * [(1 + r)^n - 1] / r
Where:
- PMT is the payment made at each compounding period.
- r is the interest rate per compounding period.
- n is the total number of compounding periods.
In this case, the payment (PMT) is $2,400, the interest rate (r) is 1.35% (expressed as a decimal, so 0.0135), and the annuity is compounded monthly for 7 years.
First, let's calculate the number of compounding periods:
Since the annuity is compounded monthly and the duration is 7 years, there are 7 * 12 = 84 compounding periods.
Now, we can substitute the values into the formula and calculate the future value:
Future Value = $2,400 * [(1 + 0.0135)^84 - 1] / 0.0135
Using a calculator, the future value is approximately:
Future Value ≈ $2,400 * [1.0135^84 - 1] / 0.0135
Future Value ≈ $2,400 * [2.3109 - 1] / 0.0135
Future Value ≈ $2,400 * 1.3109 / 0.0135
Future Value ≈ $2,400 * 97.0704
Future Value ≈ $232,969.76
Therefore, the future value of the ordinary annuity with a payment of $2,400, an interest rate of 1.35% compounded monthly, and a duration of 7 years is approximately $232,969.76.