Shawn Bixby borrowed $22,000 on a 150-day, 13% note. After 75 days, Shawn paid $2,500 on the note. On day 106, Shawn paid an additional $4,500. Use ordinary interest. What is the total interest and ending balance due?

Question

Shawn Bixby borrowed $22,000 on a 150-day, 13% note. After 75 days, Shawn paid $2,500 on the note. On day 106, Shawn paid an additional $4,500. Use ordinary interest. What is the total interest and ending balance due?

Answer 1

To find the total interest and ending balance due on a loan, we need to calculate the interest for each payment and apply it to the remaining principal.

Let's break down the given information step by step:

1. Loan amount: $22,000
2. Loan term: 150 days
3. Interest rate: 13%
4. Payment 1: After 75 days, Shawn paid $2,500 on the note.
5. Payment 2: On day 106, Shawn paid an additional $4,500.

First, we calculate the interest and update the remaining principal after Payment 1.

Step 1: Calculate interest for Payment 1
Interest = Principal * Rate * Time
Principal for Payment 1 = Initial Loan Amount - Payment 1
Interest for Payment 1 = Principal for Payment 1 * Rate * Time
Time for Payment 1 = 75 days (the time since the loan was borrowed until Payment 1)
Rate = 13% expressed as a decimal = 0.13

Principal for Payment 1 = $22,000 - $2,500 = $19,500
Interest for Payment 1 = $19,500 * 0.13 * (75/150) = $1,012.50

Remaining Principal after Payment 1 = Principal for Payment 1 + Interest for Payment 1 = $19,500 + $1,012.50 = $20,512.50

Next, we calculate the interest and update the remaining principal after Payment 2.

Step 2: Calculate interest for Payment 2
Interest = Principal * Rate * Time
Principal for Payment 2 = Remaining Principal after Payment 1 - Payment 2
Interest for Payment 2 = Principal for Payment 2 * Rate * Time
Time for Payment 2 = 106 days (the time since the loan was borrowed until Payment 2)

Principal for Payment 2 = $20,512.50 - $4,500 = $16,012.50
Interest for Payment 2 = $16,012.50 * 0.13 * (106/150) = $1,593.81

Remaining Principal after Payment 2 = Principal for Payment 2 + Interest for Payment 2 = $16,012.50 + $1,593.81 = $17,606.31

Finally, we calculate the total interest and the ending balance due.

Total Interest = Interest for Payment 1 + Interest for Payment 2 = $1,012.50 + $1,593.81 = $2,606.31

Ending Balance Due = Remaining Principal after Payment 2 + Total Interest = $17,606.31 + $2,606.31 = $20,212.62

Therefore, the total interest on the loan is $2,606.31, and the ending balance due is $20,212.62.

Shawn Bixby borrowed $22,000 on a 150-day, 13% note. After 75 days, Shawn paid $2,500 on the note. On day 106, Shawn paid an additional $4,500. Use ordinary interest. What is the total interest and ending balance due?

2551.61

To find the total interest and ending balance due on a loan, we need to calculate the interest for each payment and apply it to the remaining principal.