Mr. Michaluk has a $50,000 personal (revolving) line of credit with the Canadian Imperial Bank of Commerce (CIBC). The loan is on a demand basis at a floating rate of prime plus 1.5%. On the fifteenth of each month, a payment equal to the greater of $100 or 3% of the combined principal and accrued interest is deducted from his chequing account. The principal balance after a payment on September 15 stood at $23,465.72. Prepare the loan repayment schedule from September 15 up to and including the payment on January 15. Assume that he makes the minimum payments and the prime rate remains at 5.25%.
To prepare the loan repayment schedule, we need to calculate the interest and principal components of each payment. Let's break down the steps:
Step 1: Calculate the interest rate
The floating rate is prime plus 1.5%, so the interest rate is 5.25% (prime rate) + 1.5% = 6.75%.
Step 2: Calculate the interest for the period
For the repayment schedule, we need to calculate the interest from the principal balance after September 15 until each payment date.
- September 15 to October 15 (30 days): $23,465.72 * (6.75% / 365) * 30 = $343.22 (approximately)
- October 15 to November 15 (31 days): $23,465.72 * (6.75% / 365) * 31 = $356.90 (approximately)
- November 15 to December 15 (30 days): $23,465.72 * (6.75% / 365) * 30 = $343.22 (approximately)
- December 15 to January 15 (31 days): $23,465.72 * (6.75% / 365) * 31 = $356.90 (approximately)
Step 3: Calculate the principal component for each payment
The payment amount is the greater of $100 or 3% of the combined principal and accrued interest.
- September 15: $100
- October 15: $23,465.72 * 0.03 = $703.97
- November 15: $23,465.72 * 0.03 = $703.97
- December 15: $23,465.72 * 0.03 = $703.97
- January 15: $23,465.72 * 0.03 = $703.97
Step 4: Calculate the remaining principal balance after each payment
Subtract the principal component for each payment from the principal balance after September 15 to determine the remaining principal balance.
- September 15: $23,465.72 - $100 = $23,365.72
- October 15: $23,365.72 - $703.97 = $22,661.75
- November 15: $22,661.75 - $703.97 = $21,957.78
- December 15: $21,957.78 - $703.97 = $21,253.81
- January 15: $21,253.81 - $703.97 = $20,549.84
The loan repayment schedule from September 15 up to and including the payment on January 15 is as follows:
Date | Payment Amount | Interest | Principal | Remaining Principal Balance
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September 15 | $100 | $343.22 | $100 | $23,365.72
October 15 | $703.97 | $356.90 | $703.97 | $22,661.75
November 15 | $703.97 | $343.22 | $703.97 | $21,957.78
December 15 | $703.97 | $343.22 | $703.97 | $21,253.81
January 15 | $703.97 | $356.90 | $703.97 | $20,549.84
Please note that the interest amounts are rounded for simplicity, but the repayment schedule should use the exact amounts for accurate calculations.
To prepare the loan repayment schedule for Mr. Michaluk from September 15 up to and including the payment on January 15, we need to calculate the interest for each month, the payment amount, and the remaining principal balance. Here are the steps:
1. Calculate the interest for each month:
- October interest: $23,465.72 * (5.25% + 1.5%) / 12 = $139.84
- November interest: $23,465.72 * (5.25% + 1.5%) / 12 = $139.84
- December interest: $23,465.72 * (5.25% + 1.5%) / 12 = $139.84
- January interest: $23,465.72 * (5.25% + 1.5%) / 12 = $139.84
2. Calculate the payment amount for each month:
- October payment: Max($100, 3% * ($23,465.72 + $139.84)) = Max($100, $724.07) = $724.07
- November payment: Max($100, 3% * ($23,465.72 + $139.84 + $139.84)) = Max($100, $742.07) = $742.07
- December payment: Max($100, 3% * ($23,465.72 + $139.84 + $139.84 + $139.84)) = Max($100, $760.07) = $760.07
- January payment: Max($100, 3% * ($23,465.72 + $139.84 + $139.84 + $139.84 + $139.84)) = Max($100, $778.07) = $778.07
3. Calculate the remaining principal balance after each payment:
- October remaining balance: $23,465.72 + $139.84 - $724.07 = $22,881.49
- November remaining balance: $22,881.49 + $139.84 - $742.07 = $22,278.26
- December remaining balance: $22,278.26 + $139.84 - $760.07 = $21,657.03
- January remaining balance: $21,657.03 + $139.84 - $778.07 = $21,019.80
The loan repayment schedule is as follows:
September 15: Remaining balance - $23,465.72
October 15: Payment - $724.07, Remaining balance - $22,881.49
November 15: Payment - $742.07, Remaining balance - $22,278.26
December 15: Payment - $760.07, Remaining balance - $21,657.03
January 15: Payment - $778.07, Remaining balance - $21,019.80