Installment Loan Payoff Calculator

What is an Installment Loan?

An installment loan is a type of loan where a borrower receives a specific amount of money and agrees to repay it, plus interest, in a series of regular payments (or installments) over a set period. Common examples include mortgages, auto loans, and personal loans.

The Formula for Installment Loan Payments

The formula used to calculate the monthly payment for an installment loan is:

\[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]

Where:

• \(P\) = Monthly payment
• \(L\) = Loan amount
• \(r\) = Monthly interest rate (annual rate divided by 12)
• \(n\) = Total number of months in the loan term

Step-by-Step Calculation

1. Calculate the monthly interest rate: \[r = \frac{\text{Annual Interest Rate}}{12}\]
2. Apply the formula to calculate the monthly payment.
3. Calculate total payment: \[\text{Total Payment} = \text{Monthly Payment} \times \text{Number of Months}\]
4. Calculate total interest: \[\text{Total Interest} = \text{Total Payment} - \text{Loan Amount}\]

Example Calculation

Let's calculate the monthly payment for a $10,000 loan at 5% annual interest for 3 years:

1. \(r = \frac{5\%}{12} = 0.004167\)
2. \(P = 10000 \times \frac{0.004167(1+0.004167)^{36}}{(1+0.004167)^{36}-1} = 299.71\)
3. Total Payment = $299.71 × 36 = $10,789.56
4. Total Interest = $10,789.56 - $10,000 = $789.56

Visual Representation

The green portion represents the principal ($10,000), while the red portion shows the total interest ($789.56) over the life of the loan.