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What is the total payment required to pay off a promissory note issued for [tex]$\$750.00$[/tex] at [tex]6\%[/tex] ordinary interest and a 90-day term?

Round to the nearest cent.

Total payment: [tex]\$[?][/tex]


Sagot :

To determine the total payment required to pay off a promissory note issued for [tex]$750.00 at 6% ordinary interest over a 90-day term, follow these detailed steps: ### Step 1: Understand key terms and formula We need to calculate the interest on the promissory note using simple interest formula: \[ \text{Interest} = \text{Principal} \times \text{Annual Interest Rate} \times \frac{\text{Term in Days}}{\text{Days in a Year}} \] In this problem: - Principal (P) = $[/tex]750.00
- Annual Interest Rate (r) = 6% = 0.06 (as a decimal)
- Term in Days (t) = 90
- Ordinary interest calculation uses 360 days in a year

### Step 2: Apply the values to the formula

First, compute the interest:

[tex]\[ \text{Interest} = 750.00 \times 0.06 \times \frac{90}{360} \][/tex]

### Step 3: Calculate the interest

[tex]\[ \text{Interest} = 750.00 \times 0.06 \times 0.25 \][/tex]
[tex]\[ \text{Interest} = 750.00 \times 0.015 \][/tex]
[tex]\[ \text{Interest} = 11.25 \][/tex]

So, the interest for the term is [tex]$11.25. ### Step 4: Calculate the total payment required Add the interest to the principal to find the total payment required: \[ \text{Total Payment} = \text{Principal} + \text{Interest} \] \[ \text{Total Payment} = 750.00 + 11.25 \] \[ \text{Total Payment} = 761.25 \] ### Step 5: Round to the nearest cent (if necessary) The total payment, in this case, is already in two decimal places, so no further rounding is needed. ### Final Answer: The total payment required to pay off the promissory note issued for $[/tex]750.00 at 6% ordinary interest over a 90-day term is:

[tex]\[ \boxed{761.25} \][/tex]