You decide to take out an ordinary loan of $30,000 at 4%, on a 90 day note.
In 45 days you decide to make a payment of $10,000 on the loan. What is your new principal? Expaln how you got answer.
How much did you pay at the end of the loan overall? How does this differ from how much you would have paid overall had you not made a payment of $10,000 after 45 days?
To find the new principal after making a payment of $10,000 on the loan after 45 days, we need to calculate the interest accrued during that period and subtract it from the original principal.
Step 1: Calculate the interest accrued in 45 days.
Interest = Principal × Rate × Time
Interest = $30,000 × 0.04 × (45/365) [since 45 days is 45/365 of a year]
Interest = $1465.75
Step 2: Subtract the interest from the original principal to find the new principal.
New Principal = Original Principal - Interest
New Principal = $30,000 - $1465.75
New Principal = $28,534.25
So, the new principal after making a payment of $10,000 on the loan after 45 days is $28,534.25.
To find out how much was paid overall at the end of the loan, we need to calculate the remaining principal after the 90-day period.
Step 1: Calculate the interest accrued in 90 days.
Interest = Principal × Rate × Time
Interest = $28,534.25 × 0.04 × (90/365) [since 90 days is 90/365 of a year]
Interest = $703.93
Step 2: Subtract the interest from the new principal to find the remaining principal after 90 days.
Remaining Principal = New Principal - Interest
Remaining Principal = $28,534.25 - $703.93
Remaining Principal = $27,830.32
Therefore, at the end of the loan, the overall payment made will be $27,830.32.
If you had not made the payment of $10,000 after 45 days, the remaining principal at the end of the loan would still be $27,830.32. However, the total payment made overall would have been higher as you would have paid the accrued interest on the $10,000 for the remaining 45 days of the loan term.
To get the answer to the first question, let's break it down step by step.
1. Start with an ordinary loan of $30,000 at 4% interest rate on a 90-day note. This means that you borrowed $30,000 and will pay back the principal amount plus interest over a period of 90 days.
2. The interest rate is 4%, which means you will be charged 4% of the loan amount as interest. To calculate the interest, multiply the principal amount ($30,000) by the interest rate (0.04):
Interest = $30,000 * 0.04 = $1,200
3. The interest is typically calculated over the entire loan period, but since you made a payment after 45 days, we need to adjust the interest accordingly. The remaining loan balance after 45 days will be the original principal minus the payment made:
Remaining balance = $30,000 - $10,000 = $20,000
4. Since you only paid interest for the first 45 days, we need to calculate the interest for the remaining 45 days. Divide the interest calculated earlier by 90 (total loan days) and multiply it by the remaining days (45):
Remaining interest = ($1,200 / 90) * 45 = $600
5. Add the remaining interest to the remaining balance to get the new principal amount:
New principal = $20,000 + $600 = $20,600
So, your new principal after making a payment of $10,000 on the loan after 45 days is $20,600.
Moving on to the second question about the overall payment:
To calculate the overall payment at the end of the loan, you need to consider the interest accrued over the entire 90-day period.
1. Calculate the interest for the entire 90 days using the original principal of $30,000:
Overall interest = $30,000 * 0.04 = $1,200
2. Add the overall interest to the principal amount:
Overall payment = $30,000 + $1,200 = $31,200
So, if you had not made the payment of $10,000 after 45 days, your overall payment at the end of the loan would have been $31,200.
By making the payment of $10,000 after 45 days, you reduced the remaining balance of the loan and, as a result, reduced the total interest paid. Hence, the overall payment is lower than it would have been without the early payment.