Question: How much was received if a P88,500 loan was made and will mature after 3 years and 200 days with a discount rate of 1.75%? Round-off to 2 Decimal Places
1. **State the problem:**
We need to find the amount received from a loan of $88500$ that matures after $3$ years and $200$ days with a discount rate of $1.75\%$.
2. **Understand the formula:**
The formula for the proceeds received from a discounted loan is:
$$\text{Proceeds} = \frac{\text{Maturity Value}}{1 + d \times t}$$
where $d$ is the discount rate per year (in decimal), and $t$ is the time in years.
3. **Convert time to years:**
Since $200$ days is part of the time, convert it to years:
$$t = 3 + \frac{200}{365} = 3 + 0.5479 = 3.5479 \text{ years}$$
4. **Convert discount rate to decimal:**
$$d = \frac{1.75}{100} = 0.0175$$
5. **Calculate the denominator:**
$$1 + d \times t = 1 + 0.0175 \times 3.5479 = 1 + 0.06209 = 1.06209$$
6. **Calculate the proceeds:**
$$\text{Proceeds} = \frac{88500}{1.06209}$$
7. **Simplify the fraction:**
$$\text{Proceeds} = \frac{88500}{\cancel{1.06209}} \approx 83307.68$$
8. **Final answer:**
The amount received is approximately $83307.68$ rounded to 2 decimal places.