Steve Perry borrowed $80,000 at 12% ordinary interest for 60 days. On day 20 of the loan, Steve made a partial payment of $6,000. What is the new maturity value (in $) of the loan? (Enter a number. Round your answer to two decimal places.)
Well, it seems like Steve Perry has borrowed quite a bit! Let's break it down.
First, we need to calculate the interest on the loan for the full 60 days. The formula for simple interest is: Interest = Principal * Rate * Time.
So, the interest for the full loan period is: Interest = $80,000 * 0.12 * (60/365).
Now, Steve made a partial payment of $6,000 on day 20. This means there are 40 days left on the loan.
To find the new maturity value, we subtract the partial payment from the initial loan amount, and then add the interest for the remaining period.
The new maturity value is: $80,000 - $6,000 + (Interest * 40/60).
Calculating this, the new maturity value of the loan is $80,000 - $6,000 + ($80,000 * 0.12 * (40/60)) = $80,000 - $6,000 + ($80,000 * 0.12 * (2/3)).
After crunching the numbers, the new maturity value of the loan is approximately $80,000 - $6,000 + $6,400 = $80,400.
So, the new maturity value of the loan is $80,400. Keep in mind, though, that my calculations are just as funny as a clown juggling bananas, so please double-check them!
To find the new maturity value of the loan after the partial payment, we need to calculate the interest on the remaining balance for the remaining period.
Step 1: Calculate the remaining balance
The remaining balance after the partial payment is the original loan amount minus the partial payment.
Remaining balance = $80,000 - $6,000 = $74,000
Step 2: Calculate the interest on the remaining balance
To calculate the interest, we use the formula: Interest = Principal × Rate × Time
The principal is the remaining balance ($74,000), the rate is 12% (in decimal form, 0.12), and the time is the remaining period, which is 60 days - 20 days = 40 days.
Interest = $74,000 × 0.12 × (40/365) [Converting the time to a fraction of a year]
Step 3: Calculate the new maturity value
The new maturity value is the remaining balance plus the interest.
New maturity value = Remaining balance + Interest
Calculating the interest:
Interest = $74,000 × 0.12 × (40/365) = $1,600.00 (rounded to two decimal places)
Calculating the new maturity value:
New maturity value = $74,000 + $1,600.00 = $75,600.00
Therefore, the new maturity value of the loan after the partial payment is $75,600.00.
To find the new maturity value of the loan, we first need to calculate the interest that accrues up to day 20.
Interest = Principal × Rate × Time
Principal = $80,000
Rate = 12% = 0.12
Time = 20/360 (assuming a 360-day year)
Interest = $80,000 × 0.12 × (20/360) = $1,066.67 (rounded to two decimal places)
Now, subtract the partial payment of $6,000 from the original loan amount:
New Principal = $80,000 - $6,000 = $74,000
Next, we need to calculate the interest that accrues for the remaining 40 days.
Interest = New Principal × Rate × Time
Principal = $74,000
Rate = 12% = 0.12
Time = 40/360 (assuming a 360-day year)
Interest = $74,000 × 0.12 × (40/360) = $977.78 (rounded to two decimal places)
Finally, add the interest accrued on day 20 to the interest accrued for the remaining 40 days to get the total interest:
Total Interest = $1,066.67 + $977.78 = $2,044.45 (rounded to two decimal places)
The new maturity value is the sum of the partial payment and the total interest:
New Maturity Value = $6,000 + $2,044.45 = $8,044.45 (rounded to two decimal places)
Therefore, the new maturity value of the loan is $8,044.45.