To calculate the total interest paid after two years on a business loan with an outstanding balance of $50,000 and an annual interest rate of 10%, we'll first need to determine the monthly interest rate and then the total payments made over the two-year period.
1. Calculate the Monthly Interest Rate
The annual interest rate is 10%, so the monthly interest rate can be calculated as follows:
\[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} = \frac{10%}{12} = \frac{0.10}{12} \approx 0.008333 \]
2. Find Monthly Payments using Amortization Formula
Assuming Tom will pay the loan off in equal monthly installments, we can use the formula for monthly payments on a loan:
\[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \( M \) = total monthly payment
- \( P \) = principal amount (loan amount)
- \( r \) = monthly interest rate
- \( n \) = number of payments (months)
In this case, \( P = 50,000 \), \( r \approx 0.008333 \), and \( n = 24 \) (2 years × 12 months).
Plugging the values into the formula:
\[ M = 50000 \frac{0.008333(1 + 0.008333)^{24}}{(1 + 0.008333)^{24} - 1} \]
Calculating \( (1 + 0.008333)^{24} \):
\[ (1 + 0.008333)^{24} \approx 1.22039 \]
Now substitute this back into the payment formula:
\[ M = 50000 \frac{0.008333 \times 1.22039}{1.22039 - 1} \] \[ M = 50000 \frac{0.010184(1.22039)}{0.22039} \] \[ M = 50000 \frac{0.010184 \times 1.22039}{0.22039} \approx 2311.77 \]
3. Calculate Total Payments Over Two Years
Now, we calculate the total payments made over two years:
\[ \text{Total Payments} = M \times n = 2311.77 \times 24 \approx 55482.53 \]
4. Calculate Total Interest Paid
Finally, to find the total interest paid, we can subtract the principal from the total payments:
\[ \text{Total Interest Paid} = \text{Total Payments} - P \] \[ \text{Total Interest Paid} = 55482.53 - 50000 \approx 5482.53 \]
Thus, the total interest paid after two years would be approximately $5,482.53.
1 answer