you take out a loan for $20,000 simple interest loan at 4% on August 21 and in 45 days you pay off $8,000 of the loan. What is your new principal?
P = Po + Po(0.04/360)*45
20000 + 20000(0.04/360)*45 = $20,100 after 45 days.
Bal. = 20100-8000 = $12,100
To calculate the new principal amount, we need to understand how simple interest works and how it affects the loan.
First, let's define some terms:
- Principal: The original amount you borrowed, which is $20,000 in this case.
- Interest Rate: The rate at which interest is charged, which is 4% or 0.04 in decimal form.
- Time Period: The duration for which the interest is charged, which is 45 days.
To calculate the interest accrued on the initial loan for the given time period, we can use the formula:
Interest = Principal * Interest Rate * Time
In this case, the interest accrued on the loan is:
Interest = $20,000 * 0.04 * (45/365)
To calculate the new principal after paying off $8,000, we subtract the repayment amount from the original principal:
New Principal = Principal - Repayment Amount
New Principal = $20,000 - $8,000
Now, we can calculate the new principal by subtracting the interest accrued during the 45-day period from the previous result:
New Principal = New Principal - Interest
Let's calculate the interest and obtain the new principal value step by step:
Interest = $20,000 * 0.04 * (45/365)
Interest = $98.63
New Principal = $20,000 - $8,000
New Principal = $12,000
New Principal = $12,000 - $98.63
New Principal ≈ $11,901.37
Therefore, the new principal amount after paying off $8,000 of the loan is approximately $11,901.37.