Janet Jones borrowed $3,000 on 90-day 12 percent note. Janet paid $250 toward the note on day 35. On day 80 she paid an additional $400. Using the U.S. Rule her adjusted balance after her first payments is:
Answer: $2,785
Please do step by step. Thank you.
1. Find out the interest after 35 days:
Interest = Principal × Time × Rate
Here, Principal = $3,000, Time = 35 days (note: since we are dealing in days, the time period will be in days) and Rate = 12/100 per year
First, convert 35 days into years (assume 360 days in a year),
35 days = 35/360 years = 7/72 years
Now, we find the interest:
Interest = 3000 × 7/72 × 0.12 = $35
2. Find out the adjusted balance after first payment:
Adjusted balance after 35 days = Principal + Interest - First payment
Adjusted balance after 35 days = $3,000 + $35 - $250 = $2,785
So the adjusted balance after her first payment is $2,785.
Step 1: Calculate the interest accrued from day 35 to day 80.
To calculate the interest accrued between day 35 and day 80, we need to find the number of days between these two dates.
Days between day 35 and day 80 = 80 - 35 = 45 days
Step 2: Calculate the interest accrued from day 35 to day 80 using the U.S. Rule.
The U.S. Rule calculates interest based on a 360-day year.
Interest accrued = (Principal * Interest rate * Days) / 360
Interest accrued = (3000 * 0.12 * 45) / 360
Interest accrued = 540 / 360
Interest accrued = $1.50
Step 3: Subtract the interest accrued from the payment made on day 35.
Adjusted balance = Principal - Payment + Interest accrued
Adjusted balance = 3000 - 250 + 1.50
Adjusted balance = 2749 + 1.50
Adjusted balance = $2,750.50
Step 4: Subtract the payment made on day 80 from the adjusted balance.
Adjusted balance = Adjusted balance - Payment
Adjusted balance = 2750.50 - 400
Adjusted balance = $2,350.50
Therefore, using the U.S. Rule, the adjusted balance after the first payment is $2,350.50.
To find the adjusted balance after the first payments using the U.S. Rule, follow these steps:
Step 1: Find the interest on the original principal for the entire period of the note.
The formula to calculate the interest is: Interest = Principal x Rate x Time
Principal = $3,000
Rate = 12% (convert to decimal by dividing by 100: 12/100 = 0.12)
Time = 90 days
Interest = $3,000 x 0.12 x (90/365)
Interest = $87.12
Step 2: Subtract the interest from the first payment made on day 35.
Payment on day 35 = $250
Adjusted Principal = Principal - Payment
Adjusted Principal = $3,000 - $250
Adjusted Principal = $2,750
Step 3: Calculate the remaining balance after the first payment.
Remaining Balance = Adjusted Principal + Interest
Remaining Balance = $2,750 + $87.12
Remaining Balance = $2,837.12
Step 4: Subtract the second payment made on day 80.
Payment on day 80 = $400
Adjusted Balance = Remaining Balance - Payment
Adjusted Balance = $2,837.12 - $400
Adjusted Balance = $2,437.12
Therefore, the adjusted balance after the first payments using the U.S. Rule is $2,437.12.