Certainly! Let's tackle each part of the problem with a detailed solution.
### 14.1.1 Calculate the Monthly Interest Rate as a Percentage
Let's calculate the monthly interest rates for the first two months:
Month 1:
- Interest: \[tex]$86.99
- Initial Balance: \$[/tex]1923.81
The monthly interest rate for Month 1 is:
[tex]\[ \text{Interest Rate for Month 1} = \left( \frac{\text{Interest}}{\text{Balance}} \right) \times 100 = \left( \frac{86.99}{1923.81} \right) \times 100 \approx 4.52\% \][/tex]
Month 2:
- Interest: \[tex]$44.89
- Balance after first payment: \$[/tex]77.54
The monthly interest rate for Month 2 is:
[tex]\[ \text{Interest Rate for Month 2} = \left( \frac{\text{Interest}}{\text{Balance}} \right) \times 100 = \left( \frac{44.89}{77.54} \right) \times 100 \approx 57.89\% \][/tex]
So, the calculated monthly interest rates are approximately:
- Month 1: 4.52%
- Month 2: 57.89%
### 14.1.2 Calculate the Real Cost of the Loan
To determine the real cost of the loan, we need to consider the total payments made and the total interest incurred over the term of the loan.
Total Interest Incurred:
[tex]\[ \text{Total Interest} = 86.99 + 44.89 + 1.81 = 133.69 \][/tex]
Total Payments Made:
Assuming "C" as the final payment that completely pays off the remaining balance:
[tex]\[ \text{Total Payments} = 1891.16 + 1891.16 + 1891.16 = 5673.48 \][/tex]
Note: In a real scenario, "C" would be equal to the remaining balance after the second payment, but given the structure, let's proceed with given amounts.
Loan Principal:
[tex]\[ \text{Loan Principal} = 1923.81 \][/tex]
To find the Real Cost of the Loan:
[tex]\[ \text{Real Cost of the Loan} = \text{Total Payments} + \text{Total Interest} - \text{Loan Principal} \][/tex]
[tex]\[ \text{Real Cost of the Loan} = 5673.48 + 133.69 - 1923.81 = 3883.36 \][/tex]
Therefore, the real cost of the loan is \[tex]$3883.36.
### Summary:
- Monthly Interest Rate:
- Month 1: \(\approx 4.52\%\)
- Month 2: \(\approx 57.89\%\)
- Real Cost of the Loan: \$[/tex]3883.36
