For your pension fund, you save $160 at the end of every month for the next 30 years. The return is 6% (after tax) per annum and your saving will be compounded monthly. How much will you get at the end of year 30?

(Notes: Use 3 digits after decimal point)

This problem involves calculating the future value of an ordinary annuity, where regular contributions are made at the end of each month. We will use the future value formula for an ordinary annuity, given that the contributions are compounded monthly:

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

Where:
- $ P $ = payment per period (\$160)
- $ r $ = monthly interest rate (annual rate / 12)
- $ n $ = total number of payments (years × 12)

### Step-by-Step Calculation:

1. **Identify the parameters:**
   - $ P = 160 $ (monthly payment)
   - Annual interest rate = 6%, so monthly interest rate $ r = \frac{6\%}{12} = 0.005 $
   - $ n = 30 \times 12 = 360 $ (total payments)

2. **Substitute into the formula:**

\[
FV = 160 \times \left(\frac{(1 + 0.005)^{360} - 1}{0.005}\right)
\]

3. **Calculate the compound factor:**

\[
(1 + 0.005)^{360} \approx 6.02258
\]

4. **Solve for $ FV $:**

\[
FV = 160 \times \left(\frac{6.02258 - 1}{0.005}\right)
\]
\[
FV = 160 \times \left(\frac{5.02258}{0.005}\right)
\]
\[
FV = 160 \times 1004.516
\]
\[
FV \approx 160 \times 1004.516 \approx 160722.585
\]

### Final Answer:
The amount you will have at the end of 30 years is approximately **\$160,722.585**.

Would you like more details or have any other questions?

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Here are 5 related questions to expand your understanding:
1. What would be the future value if the contributions were made at the beginning of each month instead?
2. How would the future value change if the interest rate was 5% instead of 6%?
3. What if the saving duration was only 20 years? How would that affect the total amount?
4. How much total interest will you earn after 30 years?
5. How would the calculation change if the compounding was quarterly instead of monthly?

**Tip:** Always double-check if the payments are made at the end or beginning of each period as it changes the future value calculation.

For your pension fund, you save $160 at the end of every month for the next 30 years. The return is 6% (after tax) per annum and your saving will be compounded monthly. How much will you get at the end of year 30?

Explore the future value of saving $160 monthly for 30 years at a 6% annual interest rate, compounded monthly. Understand the future value formula of an ordinary annuity, key steps in solving the problem, and the impact of compound interest. Suitable for high school students or anyone studying financial mathematics.

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