Loan Calculator

Many consumer loans fall into this category. They have regular payments that are amortized uniformly over their lifetime. Routine payments are made on principal and interest until the loan reaches maturity (is entirely paid off). Some of the most familiar amortized loans include mortgages, car loans, student loans, and personal loans.

• Principal ($P$): The initial size of the loan. This is the amount of money you are borrowing.
• Interest Rate ($r$): Nearly all loan structures include interest, which is the profit that banks or lenders make on loans. Interest rate is the percentage of a loan paid by borrowers to lenders.
• Loan Term ($n$): A loan term is the duration of the loan, given that required minimum payments are made each month. The longer the term, the more interest will be accrued over time, raising the total cost of the loan for borrowers, but reducing the periodic payments.

To calculate the fixed monthly payment ($M$) required to fully amortize a loan of Principal ($P$) over $n$ months at a monthly interest rate of $r$:

$M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$

If you want to know the Principal based on a known Monthly Payment:

$P = M \frac{(1 + r)^n - 1}{r(1 + r)^n}$

And if you want to find the required number of months:

$n = \frac{-\log(1 - \frac{rP}{M})}{\log(1+r)}$

Our tool generates an interactive Amortization Schedule visualizing how the remaining balance decreases over time, and a Pie Chart comparing the total principal to the total interest paid.