Christina Hercher borrowed $50,000 on a 90 day, 8 percent note. Christina paid $3,000 toward the note on day 40. On day 60 she paid an additional $4,000 using the U>S. Rule. Christina's adjusted balance after the first payment is?
To find Christina's adjusted balance after the first payment, we need to calculate the remaining balance on the note after she made the first payment of $3,000 on day 40.
The first step is to determine the interest on the note for the first 40 days. We can use the simple interest formula:
Interest = Principal x Rate x Time
Principal: $50,000
Rate: 8% (expressed as a decimal, 0.08)
Time: 40/365 (since we use the U.S. Rule, assuming a 365-day year)
Interest = $50,000 x 0.08 x (40/365)
Interest ≈ $1,095.89 (rounded to the nearest cent)
Next, subtract the interest from the initial balance to get the remaining principal after the first payment:
Remaining principal = Initial balance - Interest
Remaining principal = $50,000 - $1,095.89
Remaining principal ≈ $48,904.11 (rounded to the nearest cent)
Now, let's determine the interest on the remaining principal for the next 20 days (day 41 to day 60). The interest rate remains the same (8%), and the time is 20/365:
Interest = Remaining principal x Rate x Time
Interest = $48,904.11 x 0.08 x (20/365)
Interest ≈ $897.46 (rounded to the nearest cent)
Finally, subtract the interest from the remaining principal to get Christina's adjusted balance after the first payment:
Adjusted balance = Remaining principal - Interest
Adjusted balance = $48,904.11 - $897.46
Adjusted balance ≈ $48,006.65 (rounded to the nearest cent)
Therefore, Christina's adjusted balance after her first payment is approximately $48,006.65.