A 9-months note for P80,000 with interest at 6% was written today. Find its value 3 months from today, if money is worth 5%.

To find the value of the 9-month note 3 months from today, given the conditions, we need to follow these steps:

1. **Calculate the maturity value of the note**: This is the amount the note will be worth at the end of 9 months, considering the interest rate on the note.

2. **Discount the maturity value back to 3 months from today**: Since the note is being valued 3 months from today, we need to discount the future value using the given 5% annual rate.

### Step 1: Calculate the maturity value of the note

The note amount is P80,000, and it earns 6% interest over 9 months. 

First, we calculate the interest earned:
\[ \text{Interest} = P80,000 \times \left( \frac{6\%}{100\%} \right) \times \left( \frac{9}{12} \right) \]

\[ \text{Interest} = P80,000 \times 0.06 \times 0.75 \]

\[ \text{Interest} = P3,600 \]

So, the maturity value \( M \) of the note is:
\[ M = \text{Principal} + \text{Interest} \]

\[ M = P80,000 + P3,600 \]

\[ M = P83,600 \]

### Step 2: Discount the maturity value back to 3 months from today

Now, we need to find the present value of P83,600 three months from today using the discount rate of 5%.

First, we find the monthly discount rate:
\[ \text{Monthly Discount Rate} = \frac{5\%}{12} = \frac{0.05}{12} \approx 0.004167 \]

The number of months from now to the note's maturity is 6 months (since 9 - 3 = 6).

The present value \( PV \) formula is:
\[ PV = \frac{M}{(1 + \text{rate})^n} \]

Where:
- \( M \) is the maturity value (P83,600)
- \( \text{rate} \) is the monthly discount rate (0.004167)
- \( n \) is the number of months (6)

\[ PV = \frac{P83,600}{(1 + 0.004167)^6} \]

\[ PV = \frac{P83,600}{(1.004167)^6} \]

\[ PV = \frac{P83,600}{1.025262} \]

\[ PV \approx P81,537.91 \]

Therefore, the value of the 9-month note 3 months from today, if money is worth 5%, is approximately **P81,537.91**.

Would you like further details or have any questions? 

Here are 5 more questions you might consider:

1. How do you calculate the present value of an annuity?
2. What is the difference between simple interest and compound interest?
3. How do you calculate the future value of a series of cash flows?
4. What is the formula for calculating the effective annual rate (EAR)?
5. How do you solve a system of linear equations using matrices?

**Tip:** When discounting future cash flows, ensure to use the correct time period and compounding frequency for accurate present value calculations.

Learn how to calculate the value of a 9-month note with interest at 6% and discounting at 5% three months from today. Follow step-by-step calculations using the Present Value formula. Suitable for college-level finance and mathematics students.

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