Questions: 1388.81(1-(1+0.06875/12)^(-20 × 12))/(0.06875/12)

Solution Steps

To solve the given mathematical expression, we need to break it down into its components and compute each part step-by-step. The expression involves calculating a fraction where both the numerator and the denominator contain several operations, including exponentiation and division.

1. Calculate the monthly interest rate by dividing the annual interest rate by 12.
2. Compute the term inside the parentheses raised to the power of -240 (which is -20 times 12).
3. Subtract this value from 1.
4. Multiply the result by 1388.81.
5. Divide the entire numerator by the monthly interest rate.

The monthly interest rate is calculated as follows: \[ \text{monthly rate} = \frac{0.06875}{12} \approx 0.0057291667 \]

Next, we compute the term \((1 + \text{monthly rate})^{-240}\): \[ \text{term} = \left(1 + 0.0057291667\right)^{-240} \approx 0.2538336424 \]

We then calculate the numerator by subtracting the term from 1 and multiplying by \(P\): \[ \text{numerator} = 1388.81 \times \left(1 - 0.2538336424\right) \approx 1036.2832991 \]

Finally, we divide the numerator by the monthly interest rate to find the result: \[ \text{result} = \frac{1036.2832991}{0.0057291667} \approx 180878.539472 \]

Final Answer