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Question 1175974: 1. Cris Adolfo borrowed Php80,000 at 10.4 % simple interest for 130 days. On day 40, July 3, of the loan, he made a partial payment of Php 12,500. He made another payment of Php 14,500 that pays Php 790.68 of interest.
a. When did Cris made the second partial payment.?
b. How much is being paid to his loan in his 2nd partial payment?
c. How much does he needs to pay on the due date?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's break down this loan problem step-by-step.
1. Calculate the Total Loan Time
Loan amount: Php 80,000
Simple interest rate: 10.4% per year
Loan term: 130 days
2. Calculate the First Partial Payment Information
First partial payment: Php 12,500
Day of first payment: Day 40 (July 3)
3. Calculate the Second Partial Payment Information
Second partial payment interest: Php 790.68
Second partial payment amount: Php 14,500
a. When did Cris make the second partial payment?
Calculate the principal remaining after the first payment:
First, we need to find the interest accrued up to day 40.
Interest accrued = Principal * Rate * Time
Interest accrued = 80,000 * 0.104 * (40/365)
Interest accrued ≈ 911.51
Amount owed on day 40 = 80,000 + 911.51 = 80911.51
Principal remaining after the first payment = 80911.51 - 12,500 = 68411.51
Calculate the number of days until the second payment:
Interest paid in the second payment = Php 790.68
Interest = Principal * Rate * Time
790.68 = 68411.51 * 0.104 * (Time/365)
790.68 = 7114.79304 * (Time/365)
Time/365 = 790.68 / 7114.79304
Time ≈ (790.68 / 7114.79304) * 365
Time ≈ 40.54 days
Since the second payment day is 40.54 days after day 40, we will round to 41 days.
Calculate the date of the second payment
Day 40 was July 3rd.
July has 31 days. 31-3=28 days remain in July.
41-28=13 days in August.
The second payment was made on August 13.
b. How much is being paid to his loan in his 2nd partial payment?
Total payment = Php 14,500
Interest paid = Php 790.68
Amount paid to principal = Total payment - Interest paid
Amount paid to principal = 14,500 - 790.68 = 13,709.32
c. How much does he need to pay on the due date?
Calculate the number of days from the second payment to the due date:
Total loan term = 130 days
Days until first payment = 40 days
Days until second payment = 40 + 41 = 81 days
Days remaining = 130 - 81 = 49 days
Calculate the remaining principal after the second payment:
Principal after first payment = 68411.51
Amount paid to principal in second payment = 13709.32
Remaining principal = 68411.51 - 13709.32 = 54702.19
Calculate the interest accrued over the remaining 49 days:
Interest = Principal * Rate * Time
Interest = 54702.19 * 0.104 * (49/365)
Interest ≈ 762.66
Calculate the final payment:
Final payment = Remaining principal + Interest
Final payment = 54702.19 + 762.66 = 55464.85
Answers:
a. Cris made the second partial payment on August 13.
b. Php 13,709.32 is being paid to his loan in his 2nd partial payment.
c. He needs to pay Php 55,464.85 on the due date.
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