Stacy took out a loan for $15,000. Her note was for 300 days at 5% ordinary interest. On day 100 she made a partial payment
of $5,000. On day 200 she made a second payment of $5,000. On day 250 she made yet a third payment of $2,500.
a. (1 point) What is the adjusted balance after the first payment has been made? 10208.33
b. (1 point) What is the adjusted balance after the second payment has been made? 5350.11
c. (1 point) What is the adjusted balance after the third payment has been made? 2887.26
d. (1 point) what is the final maturity value still owed on the loan after all payments have been made? 2907.31
e. (1/2 point) How much interest would she had paid if she had not made any payments? 625
f. (1 point) How much did she save in interest by making the payments?
Need help with F
Well, Stacy must have saved quite a bit of money by making those payments! Let's calculate how much she saved in interest.
To do that, we need to find out how much interest she would have paid if she hadn't made any payments. We know that the loan amount is $15,000, and the interest rate is 5% for 300 days.
To calculate the interest, we can use the formula Interest = Principal x Rate x Time.
So, the interest she would have paid without any payments can be calculated as:
Interest = $15,000 x 0.05 x (300/365)
Now, let me put on my mathematical clown hat and crunch the numbers for you...
Interest = $15,000 x 0.05 x (300/365) = $625
Therefore, she would have paid $625 in interest if she hadn't made any payments.
Now, to find out how much she saved in interest, we need to subtract the interest she actually paid from the interest she would have paid without any payments.
Saved Interest = Interest without payments - Interest with payments
Saved Interest = $625 - (0+0+0) [because she made payments of $5,000, $5,000, and $2,500, which reduced her balance]
So, Stacy saved $625 in interest by making the payments.
Good for her! It's always nice to save a few bucks, especially when it comes to interest payments!
To calculate how much Stacy saved in interest by making the payments, we need to find the interest she would have paid if she had not made any payments and subtract it from the total interest she actually paid.
Let's calculate the total interest she actually paid first:
Total Interest Paid = Interest on the first payment + Interest on the second payment + Interest on the third payment
Interest on the first payment:
Principal = $15,000 (original loan amount)
Time = 100 days
Rate = 5% (or 0.05 as a decimal)
Interest on the first payment = Principal * Rate * Time
= $15,000 * 0.05 * (100/365)
= $205.48
Interest on the second payment:
Principal = $9,791.67 (adjusted balance after the first payment)
Time = 100 days
Rate = 5%
Interest on the second payment = Principal * Rate * Time
= $9,791.67 * 0.05 * (100/365)
= $168.72
Interest on the third payment:
Principal = $5,791.67 (adjusted balance after the second payment)
Time = 50 days (since the third payment was made on day 250)
Rate = 5%
Interest on the third payment = Principal * Rate * Time
= $5,791.67 * 0.05 * (50/365)
= $78.04
Total Interest Paid = $205.48 + $168.72 + $78.04
= $452.24
Now, let's calculate the interest she would have paid if she hadn't made any payments:
Principal = $15,000 (original loan amount)
Time = 300 days
Rate = 5%
Interest without payments = Principal * Rate * Time
= $15,000 * 0.05 * (300/365)
= $616.44
To find out how much she saved in interest, we subtract the interest she actually paid from the interest without payments:
Savings in interest = Interest without payments - Total Interest Paid
= $616.44 - $452.24
= $164.20
Therefore, Stacy saved $164.20 in interest by making the payments.
To calculate how much Stacy saved in interest by making the payments, we need to find the difference between the total interest she would have paid if she had not made any payments and the total interest she actually paid after making the partial payments.
To find the total interest she would have paid if no payments were made, we can subtract the sum of the three payments she made from the final maturity value. This will give us the remaining principal amount that would have incurred interest for the full loan term.
Remaining principal amount (after all payments): $2,907.31 (calculated in part d)
Now, to calculate the interest she would have paid if no payments were made, we can use the formula:
Interest = Principal × Rate × Time
Principal: remaining principal amount ($2,907.31)
Rate: 5% (0.05 in decimal form)
Time: 300 days
Interest = $2,907.31 × 0.05 × 300/365
Calculating this, we find that the interest she would have paid if no payments were made is approximately $238.86.
Now, let's calculate the total interest she actually paid after making the partial payments. To do this, we can sum up the interest she paid after each partial payment.
Interest paid after the first payment:
Principal: $10,208.33 (adjusted balance after the first payment)
Rate: 5% (0.05 in decimal form)
Time: 200 days (remaining term after the first payment)
Interest = $10,208.33 × 0.05 × 200/365
Calculating this, we find that the interest paid after the first payment is approximately $279.45.
Next, let's calculate the interest paid after the second payment:
Principal: $5,350.11 (adjusted balance after the second payment)
Rate: 5% (0.05 in decimal form)
Time: 100 days (remaining term after the second payment)
Interest = $5,350.11 × 0.05 × 100/365
Calculating this, we find that the interest paid after the second payment is approximately $73.12.
Finally, let's calculate the interest paid after the third payment:
Principal: $2,887.26 (remaining principal amount after the third payment)
Rate: 5% (0.05 in decimal form)
Time: 50 days (remaining term after the third payment)
Interest = $2,887.26 × 0.05 × 50/365
Calculating this, we find that the interest paid after the third payment is approximately $34.25.
Now, to find the total interest she actually paid, we can sum up the interest paid after each partial payment:
Total Interest Paid = Interest paid after first payment + Interest paid after the second payment + Interest paid after the third payment
Total Interest Paid ≈ $279.45 + $73.12 + $34.25
Total Interest Paid ≈ $386.82
To calculate how much she saved in interest by making the payments, we subtract the total interest she actually paid ($386.82) from the total interest she would have paid if no payments were made ($238.86):
Interest Saved = Total Interest Paid if no payments were made - Total Interest Paid
Interest Saved ≈ $238.86 - $386.82
Interest Saved ≈ -$147.96
Since the result is negative, it means that Stacy did not save anything in interest by making the payments. In fact, she ended up paying more interest in total compared to not making any payments.