Interest Payment Calculator

What is an Interest Payment?

An interest payment is the cost of borrowing money, typically expressed as a percentage of the principal amount. In loans or investments, interest payments are regular payments made by the borrower to the lender, consisting of both principal and interest portions.

The Interest Payment Formula

The formula for calculating periodic interest payments is:

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

Where:

• \(P\) = Periodic payment amount
• \(L\) = Loan amount (principal)
• \(r\) = Periodic interest rate (annual rate divided by number of payment periods)
• \(n\) = Total number of payments

Step-by-Step Interest Payment Calculation

1. Determine the loan amount (L), annual interest rate, loan term, and payment frequency.
2. Calculate the periodic interest rate (r) by dividing the annual rate by the number of payments per year.
3. Calculate the total number of payments (n) by multiplying the loan term by the payment frequency.
4. Apply these values to the interest payment formula.
5. Calculate the periodic payment amount (P).
6. Multiply the periodic payment by the total number of payments to get the total amount paid.
7. Subtract the original loan amount from the total amount paid to find the total interest paid.

Example Calculation

Let's calculate the monthly payment for a $200,000 loan at 4.5% annual interest rate for 30 years:

1. \(L = \$200,000\), Annual rate = 4.5%, Term = 30 years, Payments = Monthly
2. Periodic rate: \(r = \frac{4.5\%}{12} = 0.375\%\) per month
3. Total payments: \(n = 30 \times 12 = 360\) months
4. \(P = 200000 \times \frac{0.00375(1+0.00375)^{360}}{(1+0.00375)^{360}-1} = \$1,013.37\)
5. Monthly payment = $1,013.37
6. Total amount paid = $1,013.37 × 360 = $364,813.20
7. Total interest paid = $364,813.20 - $200,000 = $164,813.20

Visual Representation

The green portion represents the principal ($200,000), and the blue portion represents the total interest paid ($164,813.20) over the life of the loan.