M=
(1+0.00375)
180
−1
200,000×0.00375(1+0.00375)
180

​

Let's break down the given expression for clarity and then solve it step by step:

You have:

\[
M = \frac{(1 + 0.00375)^{180} - 1}{200,000 \times 0.00375 \times (1 + 0.00375)^{180}}
\]

### Step-by-Step Solution

1. **Simplify the exponents**:
   - \( 1 + 0.00375 = 1.00375 \).
   - Then, calculate \( (1.00375)^{180} \).

2. **Calculate the numerator**:
   - \( (1.00375)^{180} - 1 \).

3. **Calculate the denominator**:
   - Multiply \( 200,000 \times 0.00375 \times (1.00375)^{180} \).

4. **Divide the two results** to get the value of \( M \).

Let me calculate that for you.The value of \( M \) is approximately \( 0.0006536 \).

Would you like further details on how this was calculated or have any questions?

Here are 5 related questions to expand on this concept:
1. How would changing the interest rate affect the value of \( M \)?
2. What happens if we change the number of periods in the formula?
3. How does this formula relate to the calculation of loan payments?
4. What is the purpose of compounding interest in this context?
5. How would a change in the principal amount influence the final result?

**Tip:** When dealing with exponentiation in interest-related formulas, small changes in the rate or the number of periods can have a significant impact due to compounding effects.

M = (1 + 0.00375)^{180} - 1 / (200,000 × 0.00375 × (1 + 0.00375)^{180})

This page explains how to calculate compound interest using the exponential formula M = (1 + 0.00375)^{180} - 1 / (200,000 × 0.00375 × (1 + 0.00375)^{180}). Follow the step-by-step solution and learn about exponential functions and compound interest, suitable for high school students in Grades 11-12.

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