1. Use the United States Rule and/or the Banker's Rule to determine the balance due on the loan at the date of maturity.
The effective date is the date the loan was written. A day counting table may be found in the Consumer Mathematics chapter of your textbok.
Principal: $12,000.00
Rate: 9.5%
Effective Date: March 22
Maturity Date: December 5
Partial Payment Amount: $7,000.00
Partial Payment Due: August 30
$5,127.99
$5,478.74
$5,614.52
$5,650.87
To determine the balance due on the loan at the date of maturity, we can use the United States Rule and/or the Banker's Rule.
1. United States Rule:
The United States Rule considers the number of days in a year as 360, divided into 12 equal months of 30 days each. To calculate the balance due, we need to follow these steps:
Step 1: Calculate the interest accrued from the effective date to the partial payment due date (August 30):
Number of days = 161 days (August 30 - March 22)
Interest accrued = Principal * Rate * (Number of days/360)
= 12,000 * 0.095 * (161/360)
= $535.78
Step 2: Subtract the partial payment amount from the principal:
Balance after partial payment = Principal - Partial payment amount
= 12,000 - 7,000
= $5,000
Step 3: Calculate the interest accrued from the partial payment due date to the maturity date (December 5):
Number of days = 97 days (December 5 - August 30)
Interest accrued = Balance after partial payment * Rate * (Number of days/360)
= 5,000 * 0.095 * (97/360)
= $132.74
Step 4: Calculate the total balance due at maturity:
Total balance due = Balance after partial payment + Interest accrued from partial payment period + Interest accrued from maturity period
= 5,000 + 535.78 + 132.74
= $5,668.52
2. Banker's Rule:
The Banker's Rule considers the actual number of days in a month and adjusts it for leap years. To calculate the balance due, we need to follow these steps:
Step 1: Calculate the interest accrued from the effective date to the partial payment due date (August 30):
Number of days = 161 days (August 30 - March 22)
Interest accrued = Principal * Rate * (Number of days/365)
= 12,000 * 0.095 * (161/365)
= $533.92
Step 2: Subtract the partial payment amount from the principal:
Balance after partial payment = Principal - Partial payment amount
= 12,000 - 7,000
= $5,000
Step 3: Calculate the interest accrued from the partial payment due date to the maturity date (December 5):
Number of days = 97 days (December 5 - August 30)
Interest accrued = Balance after partial payment * Rate * (Number of days/365)
= 5,000 * 0.095 * (97/365)
= $129.15
Step 4: Calculate the total balance due at maturity:
Total balance due = Balance after partial payment + Interest accrued from partial payment period + Interest accrued from maturity period
= 5,000 + 533.92 + 129.15
= $5,663.07
Therefore, the balance due on the loan at the date of maturity is approximately $5,663.07, using the Banker's Rule.