Whether you're a student or a professional, IDNLearn.com has answers for everyone. Our community provides accurate and timely answers to help you understand and solve any issue.
Sagot :
To find the adjusted balance (principal) using the U.S. Rule, we need to follow a series of steps:
1. Calculate the interest for the first 90 days:
The formula for calculating simple interest is:
[tex]\[ I = P \times r \times \frac{t}{360} \][/tex]
Given:
- Principal ([tex]\(P\)[/tex]) = \[tex]$7,000 - Annual rate (\(r\)) = 11\% (or 0.11 as a decimal) - Time (\(t\)) = 90 days \[ I_{90} = 7000 \times 0.11 \times \frac{90}{360} \] Performing the calculation: \[ I_{90} = 192.5 \] Therefore, the interest for the first 90 days is \$[/tex]192.5.
2. Calculate the new principal after the partial payment:
We need to determine the principal after accounting for the accumulated interest and subtracting the partial payment.
- Partial payment = \[tex]$1,200 Adding the interest to the principal: \[ P_{\text{new}} = 7000 + 192.5 - 1200 \] Performing the calculation: \[ P_{\text{new}} = 5992.5 \] The new principal after the partial payment is \$[/tex]5,992.5.
3. Calculate the interest for the remaining period (30 days):
The remaining period after day 90 is [tex]\(120 - 90 = 30\)[/tex] days.
Using the interest formula again with the new principal:
[tex]\[ I_{30} = P_{\text{new}} \times r \times \frac{t_{\text{remaining}}}{360} \][/tex]
Given:
- New principal ([tex]\(P_{\text{new}}\)[/tex]) = \[tex]$5,992.5 - Annual rate (\(r\)) = 11\% (or 0.11 as a decimal) - Remaining time (\(t_{\text{remaining}}\)) = 30 days \[ I_{30} = 5992.5 \times 0.11 \times \frac{30}{360} \] Performing the calculation: \[ I_{30} = 54.93125 \] Therefore, the interest for the remaining 30 days is \$[/tex]54.93125.
4. Calculate the final adjusted balance:
The final adjusted balance is the new principal plus the interest accumulated over the remaining period.
[tex]\[ P_{\text{adjusted}} = P_{\text{new}} + I_{30} \][/tex]
Performing the calculation:
[tex]\[ P_{\text{adjusted}} = 5992.5 + 54.93125 \][/tex]
Therefore, the adjusted balance is:
[tex]\[ P_{\text{adjusted}} = 6047.43125 \][/tex]
So, the adjusted balance after the first payment on day 90 is \$6,047.43125.
1. Calculate the interest for the first 90 days:
The formula for calculating simple interest is:
[tex]\[ I = P \times r \times \frac{t}{360} \][/tex]
Given:
- Principal ([tex]\(P\)[/tex]) = \[tex]$7,000 - Annual rate (\(r\)) = 11\% (or 0.11 as a decimal) - Time (\(t\)) = 90 days \[ I_{90} = 7000 \times 0.11 \times \frac{90}{360} \] Performing the calculation: \[ I_{90} = 192.5 \] Therefore, the interest for the first 90 days is \$[/tex]192.5.
2. Calculate the new principal after the partial payment:
We need to determine the principal after accounting for the accumulated interest and subtracting the partial payment.
- Partial payment = \[tex]$1,200 Adding the interest to the principal: \[ P_{\text{new}} = 7000 + 192.5 - 1200 \] Performing the calculation: \[ P_{\text{new}} = 5992.5 \] The new principal after the partial payment is \$[/tex]5,992.5.
3. Calculate the interest for the remaining period (30 days):
The remaining period after day 90 is [tex]\(120 - 90 = 30\)[/tex] days.
Using the interest formula again with the new principal:
[tex]\[ I_{30} = P_{\text{new}} \times r \times \frac{t_{\text{remaining}}}{360} \][/tex]
Given:
- New principal ([tex]\(P_{\text{new}}\)[/tex]) = \[tex]$5,992.5 - Annual rate (\(r\)) = 11\% (or 0.11 as a decimal) - Remaining time (\(t_{\text{remaining}}\)) = 30 days \[ I_{30} = 5992.5 \times 0.11 \times \frac{30}{360} \] Performing the calculation: \[ I_{30} = 54.93125 \] Therefore, the interest for the remaining 30 days is \$[/tex]54.93125.
4. Calculate the final adjusted balance:
The final adjusted balance is the new principal plus the interest accumulated over the remaining period.
[tex]\[ P_{\text{adjusted}} = P_{\text{new}} + I_{30} \][/tex]
Performing the calculation:
[tex]\[ P_{\text{adjusted}} = 5992.5 + 54.93125 \][/tex]
Therefore, the adjusted balance is:
[tex]\[ P_{\text{adjusted}} = 6047.43125 \][/tex]
So, the adjusted balance after the first payment on day 90 is \$6,047.43125.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.
