Question
The business loan disbursed in March for S/. 150,000 at an APR of 12% was agreed to be paid in 3 equal monthly installments of S/. 55,000 starting in April, however, only 1 installment was paid in April and the businessman wishes to modify his schedule by paying the entire available balance in 2 equal installments in October and November. Determine how much the fees are
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Answer to a math question The business loan disbursed in March for S/. 150,000 at an APR of 12% was agreed to be paid in 3 equal monthly installments of S/. 55,000 starting in April, however, only 1 installment was paid in April and the businessman wishes to modify his schedule by paying the entire available balance in 2 equal installments in October and November. Determine how much the fees are
Eliseo
4.6107 Answers
1. **Initial Loan & Payment Details**:
- Original Loan Amount:150,000
- Interest Rate (APR): 12%
- Monthly Interest Rate:\frac{12}{12} = 1\% = 0.01
- First Installment Paid:55,000
2. **Calculating Remaining Balance Before Re-Structuring**:
- Remaining Balance After April Payment (No Interest Considered for April):
150,000 - 55,000 = 95,000
3. **Paying the Balance in Two Equal Installments**:
- Since the loan should be cleared in two installments, simply divide the remaining balance by 2.
- Each installment:
\frac{95,000}{2} = 47,500
4. **Interest on Remaining Balance Between April and Installment Period**:
- Since there's no intermediate payment between the settled payment for April and the restructured installments in October and November, we assume interest needs to be recalculated on the unpaid balance.
- Adding accumulated interest from May to October on the remaining balance:
- Remaining Balance:95,000
- Interest accumulation over 5 months on balance:
\text{Future Value (FV)} = 95,000 \times (1 + 0.01)^5
- \text{FV} = 95,000 \times 1.0510100501 \approx 99,845.95
5. **Final Payments**:
- Divide99,845.95
\frac{99,845.95}{2} \approx 49,922.97
- Since we need to pay in two equal amounts aligning to business scenarios, we can correctly round this amount to manageable numbers relative to original debts:
- Final amount rounded: \approx S/. 50,000
So, based on unpaid interest and redistribution of the loan, suitable equal payments in general business perspectives for October and November would be calculated around S/. 50,000 each to cover any inconsistencies due to challenge beyond the direct problem stated.
- Original Loan Amount:
- Interest Rate (APR): 12%
- Monthly Interest Rate:
- First Installment Paid:
2. **Calculating Remaining Balance Before Re-Structuring**:
- Remaining Balance After April Payment (No Interest Considered for April):
3. **Paying the Balance in Two Equal Installments**:
- Since the loan should be cleared in two installments, simply divide the remaining balance by 2.
- Each installment:
4. **Interest on Remaining Balance Between April and Installment Period**:
- Since there's no intermediate payment between the settled payment for April and the restructured installments in October and November, we assume interest needs to be recalculated on the unpaid balance.
- Adding accumulated interest from May to October on the remaining balance:
- Remaining Balance:
- Interest accumulation over 5 months on balance:
-
5. **Final Payments**:
- Divide
- Since we need to pay in two equal amounts aligning to business scenarios, we can correctly round this amount to manageable numbers relative to original debts:
- Final amount rounded:
So, based on unpaid interest and redistribution of the loan, suitable equal payments in general business perspectives for October and November would be calculated around S/. 50,000 each to cover any inconsistencies due to challenge beyond the direct problem stated.
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