Lisa borrowed 8,000 on an 8% , 60 day note after 15 days she paid 2,000 on the note on day 45 she paid 1,000 on the note what is the total interest and ending balance due by the us rule of ordinary interest.
To find the total interest and ending balance due on a note using the US rule of ordinary interest, we need to follow these steps:
1. Calculate the interest for each period of time using the formula: Interest = Principal x Rate x Time
- Principal: The initial amount borrowed, which is $8,000.
- Rate: The interest rate, which is 8% or 0.08 (as a decimal).
- Time: The time period in years.
For the first interest payment, Lisa held the note for 15 days. So, we need to convert the time period to years. Since 60 days is equivalent to 2 months, which is 1/6 of a year, the time for the first interest payment is 15 / 365 ≈ 0.0411 (to 4 decimal places) years.
For the second interest payment, Lisa held the note for 30 days from the first payment to the second. So, the time for the second interest payment is 30 / 365 ≈ 0.0822 years.
2. Calculate the interest for each payment and add them up to find the total interest.
3. Subtract the total payments made from the initial principal to find the ending balance due.
Let's calculate it step by step:
1. Calculate the interest for each period:
- First interest payment: Interest₁ = $8,000 x 0.08 x 0.0411
- Second interest payment: Interest₂ = ($8,000 - $2,000) x 0.08 x 0.0822
2. Total interest = Interest₁ + Interest₂
3. Calculate the ending balance due:
- First payment: $8,000 - $2,000 = $6,000
- Second payment: $6,000 - $1,000 = $5,000
Therefore, to find the total interest and ending balance due, we need to plug in the appropriate values into the formulas:
Interest₁ = $8,000 x 0.08 x 0.0411 ≈ $26.40
Interest₂ = ($8,000 - $2,000) x 0.08 x 0.0822 ≈ $40.96
Total interest = $26.40 + $40.96 ≈ $67.36
Ending balance due = $5,000
So, the total interest is approximately $67.36 and the ending balance due is $5,000 by the US rule of ordinary interest.