Loan and Monthly Installment Calculator

Formula

With principal $P$, monthly rate $r = \text{annual rate} / 12$, and $n$ monthly payments, the level payment is

If the rate is zero the formula collapses to $M = P / n$. Total paid is $M \times n$ and total interest is $M n - P$. Each month the interest is $r \times \text{balance}$ and the rest of the payment reduces the balance.

Worked example

Loan of 200,000 at 6% for 30 years.

• $r = 0.06 / 12 = 0.005$, $n = 360$.
• $(1.005)^{-360} \approx 0.16604$, so $M = 200{,}000 \times 0.005 / (1 - 0.16604) \approx 1{,}199.10$.
• Total paid: $1{,}199.10 \times 360 \approx 431{,}676$.
• Total interest: about 231,676, more than the amount borrowed.

The first payment splits into 1,000.00 interest and 199.10 principal.

Common mistakes

• Dividing the annual rate by 12 and then also using years as $n$. The term must be in months when the rate is monthly.
• Quoting the monthly payment without the total interest. A longer term lowers the payment but raises the total cost.
• Comparing a flat-rate quote with a reducing-rate quote as if they were the same.
• Assuming extra payments are in the schedule. They shorten the loan and are not modelled here.