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Sagot :
The total cost of the loan is the sum of the amount borrowed and the interest paid over the life of the loan. In this case, we can calculate it as follows:
Monthly Interest: The interest rate is 1.5%, but it's charged monthly, so we need to convert it to a monthly rate: monthly_interest_rate = 1.5% / 12 = 0.125%
Monthly Payment for Principal: We are given that the borrower pays $300 per month to reduce the loan.
Calculate Monthly Payment: While the problem doesn't explicitly state the loan term, we are given that the loan is repaid over 18 months. We can use this information to calculate the total payment using the loan amount, monthly interest rate, and loan term with the following formula (assuming equal monthly payments):
monthly_payment = loan_amount * (monthly_interest_rate + (1 + monthly_interest_rate) ^ term) / ((1 + monthly_interest_rate) ^ term - 1)
Note: This formula is not strictly necessary to solve this specific problem, but it can be helpful for calculating monthly payments in general loan scenarios.
Total Interest Paid: Each month, the interest is calculated on the remaining loan balance. We can iterate through each month and calculate the interest paid as:
interest_payment = loan_balance * monthly_interest_rate
We can keep track of the total interest paid by adding the interest payment each month.
Total Cost: After 18 months, the loan will be paid off. The total cost of the loan is the sum of the amount borrowed and the total interest paid.
Solving without the formula:
In this specific case, we can directly calculate the total cost without needing the formula for the monthly payment since the principal payment amount is explicitly given.
Over 18 months, the total payment towards the principal will be: total_principal_payment = $300/month * 18 months = $5400
Now, we need to calculate the total interest paid over 18 months. We can do this manually for each month or use a spreadsheet, but it will be a repetitive process.
Assuming a spreadsheet is used:
We can set up a spreadsheet with columns for month number, remaining balance, interest payment (calculated using monthly interest rate and remaining balance), and principal payment. Each month, the remaining balance is reduced by the principal payment. This will automatically calculate the interest paid each month based on the decreasing balance.
After 18 months, the spreadsheet will show the total interest paid.
Total Cost:
Add the total amount borrowed ($5400) to the total interest paid to find the total cost of the loan.
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