To calculate the final monthly payment required to pay off a loan, we need to use the formula for an amortized loan with fixed payments. However, a key piece of information is missing to use that formula: the number of payments remaining or the duration of the loan.
Let's assume we have the number of payments (n) and the monthly interest rate (i). The monthly interest rate can be calculated by dividing the annual interest rate by 12. Then we can use the following formula to find the monthly payment (M), where P is the loan principal:
\[ M = \frac{P \cdot i}{1 - (1 + i)^{-n}} \]
Given that we do not have the number of payments (n), we cannot solve for M using this formula.
However, if we wanted to find out the final single monthly payment to pay off the entire loan at once, without any additional payments in the future, we don't need to amortize the loan. In this case, we would only need to consider the interest accumulated over one month.
First, let's find out the monthly interest rate:
Annual interest rate = 12%
Monthly interest rate = 12% / 12
= 1%
Converting this percentage to a decimal for calculation:
Monthly interest rate (i) = 1 / 100
= 0.01
The interest for one month on the remaining principal of $1900 would be:
Interest for one month = Principal × Monthly interest rate
= $1900 × 0.01
= $19
We add this interest to the remaining principal to find out what the final payment would need to be to pay off the loan in its entirety in a single month:
Final payment = Principal + Interest
= $1900 + $19
= $1919
Thus, if paying off the entire loan in one month including the interest accrued over that month, the final payment would be $1919. However, if the loan is to be paid off over several months, the actual monthly payment will be less than this amount, but you would need the loan term or the number of payments to calculate it. Since those details are not provided, we cannot provide a more precise answer.
