Euromart Tile Company borrowed $40,000 on April 6 for 66 days. The rate was 14% using the ordinary interest rate method. On day 25 of the loan, Euromart made a partial payment of $15,000, and on day 45 of the loan, Euromart made a second partial payment of $10,000. What was the new maturity value of the loan?
I=PRT
I=40,000*.14*25/360=$388.89 (interest)
$15,000-388.89=$14,611.11 (amt. of partial payment left to reduce the principal)
40,000-14,611.11=$25,388.89 (adjusted principal balance)
$25,388.89*.14*20/360=197.47
10,000-197.47=9802.53
25,388.89-9802.53=15,586.36
15,586.36*.14*21/360=127.29
15,586.36-127.29=$15,713.65
Maturity Value of the loan is $15,713.65
To calculate the new maturity value of the loan, we need to first calculate the remaining principal amount after each partial payment. Let's break it down step by step:
Step 1: Find the principal remaining after the first partial payment on day 25.
Remaining principal = Original principal - First partial payment
Remaining principal = $40,000 - $15,000
Remaining principal = $25,000
Step 2: Find the principal remaining after the second partial payment on day 45.
Remaining principal = Previous remaining principal - Second partial payment
Remaining principal = $25,000 - $10,000
Remaining principal = $15,000
Step 3: Calculate the interest for the remaining period.
Interest = Remaining principal * Interest rate * Time
Here, the time is the remaining number of days (66 - 45)
Interest = $15,000 * 14% * (66 - 45)/365
Interest = $15,000 * 0.14 * 21/365
Interest = $147.95
Step 4: Calculate the new maturity value.
New maturity value = Remaining principal + Interest
New maturity value = $15,000 + $147.95
New maturity value = $15,147.95
Therefore, the new maturity value of the loan is $15,147.95.
To determine the new maturity value of the loan, we need to calculate the remaining principal amount after each partial payment and then find the interest on the remaining principal for the remaining days.
Let's break down the steps:
Step 1: Calculate the remaining principal after the first partial payment.
The original principal is $40,000. After the first partial payment of $15,000 on day 25, the remaining principal is $40,000 - $15,000 = $25,000.
Step 2: Calculate the remaining principal after the second partial payment.
On day 45, Euromart made a second partial payment of $10,000, reducing the remaining principal to $25,000 - $10,000 = $15,000.
Step 3: Calculate the interest on the remaining principal.
The interest rate is 14%. We need to convert it to a decimal, so it becomes 0.14.
The loan duration was initially for 66 days, but since we need to calculate the interest for the remaining days after each partial payment, we need to subtract the number of days when the partial payment was made.
The first partial payment was made on day 25, so the remaining days for the first interest calculation would be 66 - 25 = 41 days.
The second partial payment was made on day 45, so the remaining days for the second interest calculation would be 66 - 45 = 21 days.
To calculate the interest on the remaining principal after the first partial payment:
Interest = Principal × Rate × Time
= $25,000 × 0.14 × (41/365) (using ordinary interest rate method)
To calculate the interest on the remaining principal after the second partial payment:
Interest = Principal × Rate × Time
= $15,000 × 0.14 × (21/365) (using ordinary interest rate method)
Step 4: Calculate the new maturity value.
The new maturity value is the sum of the remaining principal and the interest after each partial payment.
New Maturity Value = Remaining Principal + Interest after first partial payment + Interest after second partial payment
Let's substitute the values:
New Maturity Value = $15,000 + (Interest after first partial payment) + (Interest after second partial payment)
Finally, you can substitute the values for each step and calculate the new maturity value.