find the future value for the ordinary annuity with the given payment and interest rate.\npmt = $2,000…

Explanation:

Step1: Define variables

Let $\text{PMT} = 2000$, $r = 0.0125$, $n = 12$, $t = 2$

Step2: Calculate monthly rate

$i = \frac{r}{n} = \frac{0.0125}{12}$

Step3: Calculate total periods

$N = n \times t = 12 \times 2 = 24$

Step4: Apply future value formula

The formula for the future value of an ordinary annuity is: $$FV = \text{PMT} \times \frac{(1+i)^N - 1}{i}$$ Substitute values: $$FV = 2000 \times \frac{\left(1+\frac{0.0125}{12}\right)^{24} - 1}{\frac{0.0125}{12}}$$

Step5: Compute intermediate terms

First calculate $\left(1+\frac{0.0125}{12}\right)^{24} \approx 1.025315$ Then $(1.025315 - 1) = 0.025315$ Next, $\frac{0.025315}{\frac{0.0125}{12}} = 0.025315 \times \frac{12}{0.0125} = 24.2928$

Step6: Compute final value

$FV = 2000 \times 24.2928 = 48585.60$

Answer:

$$48585.60$