The formula used in the calculation is:
\[ \text{loan remaining} = \text{loan} \times (1 + r)^k - \left( \frac{\text{monthly payment} \times ((1 + r)^k - 1)}{r} \right) \]
This calculator computes the remaining loan balance based on the input values of loan amount, annual interest rate, loan term, and time passed since the loan was taken.
Let's assume the following:
First, convert the annual interest rate to a monthly interest rate:
\[ r = \frac{5}{100} \div 12 = 0.004167 \]
Convert the loan term and time passed to months:
\[ n = 5 \times 12 = 60 \]
\[ k = 2 \times 12 = 24 \]
Calculate the monthly payment:
\[ \text{monthly payment} = 10,000 \times 0.004167 \times (1 + 0.004167)^{60} \div ((1 + 0.004167)^{60} - 1) \approx 188.71 \]
Calculate the remaining loan balance:
\[ \text{loan remaining} = 10,000 \times (1 + 0.004167)^{24} - \left( \frac{188.71 \times ((1 + 0.004167)^{24} - 1)}{0.004167} \right) \approx 6,297 \]
Therefore, the remaining loan balance is approximately $6,297.
