Sure, let's work through the given problem step-by-step:
### Note (a):
- Date of Note: June 10
- Principal Amount: [tex]$80,000
- Interest Rate: 6%
- Term: 60 days
Interest Calculation:
The formula to calculate simple interest is:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \left(\frac{\text{Term}}{360}\right) \]
Plugging in the values:
\[ \text{Interest} = \$[/tex]80,000 \times 0.06 \times \left(\frac{60}{360}\right) \]
[tex]\[ \text{Interest} = \$80,000 \times 0.06 \times 0.1667 \][/tex]
[tex]\[ \text{Interest} = \$800 \][/tex]
Maturity Date Calculation:
Adding 60 days to June 10:
- June has 30 - 10 = 20 days left
- We need 40 more days
- Adding 40 days to June 30th lands in August 9th
So, for Note (a):
- Interest: [tex]$800
- Maturity Date: August 9
### Note (b):
- Date of Note: July 14
- Principal Amount: $[/tex]50,000
- Interest Rate: 7%
- Term: 90 days
Interest Calculation:
[tex]\[ \text{Interest} = \$50,000 \times 0.07 \times \left(\frac{90}{360}\right) \][/tex]
[tex]\[ \text{Interest} = \$50,000 \times 0.07 \times 0.25 \][/tex]
[tex]\[ \text{Interest} = \$875 \][/tex]
Maturity Date Calculation:
Adding 90 days to July 14:
- July has 31 - 14 = 17 days left
- We need 73 more days
- Adding 31 days of August leaves 42 more days
- Adding 42 days from September lands in October 12th
So, for Note (b):
- Interest: [tex]$875
- Maturity Date: October 12
### Note (c):
- Date of Note: April 27
- Principal Amount: $[/tex]12,000
- Interest Rate: 8%
- Term: 75 days
Interest Calculation:
[tex]\[ \text{Interest} = \$12,000 \times 0.08 \times \left(\frac{75}{360}\right) \][/tex]
[tex]\[ \text{Interest} = \$12,000 \times 0.08 \times 0.2083 \][/tex]
[tex]\[ \text{Interest} = \$200 \][/tex]
Maturity Date Calculation:
Adding 75 days to April 27:
- April has 30 - 27 = 3 days left
- We need 72 more days
- Adding 31 days of May leaves 41 more days
- Adding 30 days of June leaves 11 more days
- Adding 11 days from July takes us to July 11th
So, for Note (c):
- Interest: [tex]$200
- Maturity Date: July 11
### Final Answers:
- (a) Interest: \$[/tex]800; Maturity Date: August 9
- (b) Interest: \[tex]$875; Maturity Date: October 12
- (c) Interest: \$[/tex]200; Maturity Date: July 11
