To solve for the future value (FV) given the number of periods ($n$), interest rate per period ($i$), and periodic payment ($PMT$), we use the formula for the future value of an ordinary annuity:

$FV = PMT \times \left( \frac{(1 + i)^n - 1}{i} \right)$

Given:

• $n = 36$
• $i = 0.03$
• $PMT = 40$

We can substitute these values into the formula.

First, compute $(1 + i)^n$:

$(1 + 0.03)^{36}$

Next, calculate $(1 + 0.03)^{36} - 1$:

$(1.03)^{36} - 1$

Then, divide this result by $i$:

$\frac{(1.03)^{36} - 1}{0.03}$

Finally, multiply by $PMT$:

$FV = 40 \times \left( \frac{(1.03)^{36} - 1}{0.03} \right)$

Let’s compute these step by step.

1. Compute $(1 + 0.03)^{36}$:

$(1.03)^{36} \approx 2.8920$

2. Compute $(1.03)^{36} - 1$:

$2.8920 - 1 = 1.8920$

3. Divide by $i$:

$\frac{1.8920}{0.03} \approx 63.0667$

4. Multiply by $PMT$:

$40 \times 63.0667 \approx 2522.67$

Therefore, the future value $FV$ is approximately $2522.67.

Do you want details or have any questions?

Here are some related questions:

1. How does the interest rate affect the future value of an annuity?
2. What is the difference between the present value and future value of an annuity?
3. How does the number of periods impact the future value calculation?
4. Can the future value formula be applied to any type of annuity?
5. What are some practical applications of calculating the future value of an annuity?
6. How would the future value change if the payments were made at the beginning of each period (annuity due)?
7. What is the effect of compounding frequency on the future value?
8. How can we adjust the future value formula for continuous compounding?

Tip: When dealing with financial calculations, it’s helpful to use a financial calculator or spreadsheet software to ensure precision and save time on repetitive calculations.