Question

A bank made a loan of $27,000.00 on March 7 to Person X to purchase equipment for their office. The loan was secured by a demand loan subject to a variable rate of interest that was 7% on March 7. The rate of interest was raised to 7.5% effective July 1 and to 7.75% effective September 1. Person X made partial payments on the loan as follows: $1000 on May 12; $600 on June 30; and $300 on October 11. Each payment is first applied to any accumulated interest. Any remainder is then used to reduce the outstanding principal. The terms of the note require payment on October 31 of any interest not paid off by partial payments. How much must Person X pay on October 31?

Answer 1

To calculate how much Person X must pay on October 31, we first need to calculate the interest accrued on the loan at each interest rate and subtract the partial payments made. Then, we can determine the remaining balance on October 31.

1. Calculate interest from March 7 to June 30 at a 7% interest rate:

- Number of days from March 7 to June 30 = 116 days

- Interest for this period = Principal × Rate × (Days / 365)

- Interest = $27,000 × 0.07 × (116 / 365) = $853.15

2. Calculate interest from July 1 to August 31 at a 7.5% interest rate:

- Number of days from July 1 to August 31 = 62 days

- Interest for this period = Principal × Rate × (Days / 365)

- Interest = $27,000 × 0.075 × (62 / 365) = $460.27

3. Calculate interest from September 1 to October 11 at a 7.75% interest rate:

- Number of days from September 1 to October 11 = 40 days

- Interest for this period = Principal × Rate × (Days / 365)

- Interest = $27,000 × 0.0775 × (40 / 365) = $297.81

Now, let's calculate the total interest accrued:

Total Interest = $853.15 + $460.27 + $297.81 = $1,611.23

Next, subtract the partial payments made:

- $1000 on May 12

- $600 on June 30

- $300 on October 11

Total Partial Payments = $1000 + $600 + $300 = $1900

Now, calculate the remaining balance on October 31:

Remaining Balance = Loan Amount + Total Interest - Total Partial Payments

Remaining Balance = $27,000 + $1,611.23 - $1,900 = $26,711.23

Therefore, Person X must pay $26,711.23 on October 31 to cover the interest not paid off by partial payments.

Step-by-step explanation: