To determine how much you will have paid at the end of five years after borrowing $10,000, you'll need to know the interest rate and whether the loan is amortized, meaning it's paid off in regular installments, or if it's a different type of loan (like a lump sum at maturity).
Assuming it's a standard amortized loan with a specific interest rate, you can use the loan payment formula. The total amount paid will be the monthly payment multiplied by the number of months.
Formula for Monthly Payment:
The monthly payment \(M\) can be calculated using the following formula:
\[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \(P\) = principal amount (loan amount, $10,000 in this case)
- \(r\) = monthly interest rate (annual interest rate divided by 12)
- \(n\) = total number of payments (loan term in months)
Total Amount Paid:
The total amount paid over the term of the loan is:
\[ \text{Total Paid} = M \times n \]
Example Calculation:
Let's assume an interest rate of 5% per annum:
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Convert annual interest rate to monthly: \[ r = \frac{5%}{100} \div 12 \approx 0.004167 \]
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Determine the total number of payments: \[ n = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ months} \]
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Calculate the monthly payment using the formula: \[ M = 10000 \frac{0.004167(1 + 0.004167)^{60}}{(1 + 0.004167)^{60} - 1} \]
After performing the calculation, you would find \(M\) (approximately $188.71).
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Calculate the total amount paid: \[ \text{Total Paid} = M \times n \approx 188.71 \times 60 \approx 11322.60 \]
Conclusion:
If you borrow $10,000 at an interest rate of 5% over five years, you would pay approximately $11,322.60 in total by the end of the loan term. Adjust the interest rate in the calculations based on the actual rate to find your exact total payment.