Tom has a business loan with an outstanding balance of $50,000 and an annual interest rate of 10%. If he makes monthly payments, what will be the total interest paid after two years?

1 answer

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.