Loan Interest Calculator

Interest on a loan is charged on the outstanding balance, for the length of time that balance is outstanding. Everything else is a variation on that one idea.

Monthly accrual (most instalment loans):

$I = B \times \frac{r_{\text{annual}}}{12}$

Daily accrual / per diem (credit lines, payoff quotes, interest between closing and the first payment):

$I = B \times \frac{r_{\text{annual}}}{365} \times d$

where $d$ is the number of days. Some contracts use a 360-day year, which makes each daily charge slightly larger — check which convention yours uses.

Interest-only payment: pay exactly the accrued interest and the balance never moves:

$M_{\text{IO}} = B \times \frac{r_{\text{annual}}}{12}$

Nothing here is a rate quote or a lending rule. Rates, day-count conventions and qualification standards come from your lender and your jurisdiction; this page does the arithmetic on the figures you enter.

The payment

When each payment covers the interest and chips at the balance, the level payment is

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

with $r$ the monthly rate and $n$ the number of monthly payments ($30$ years $= 360$).

The total interest

$\text{total interest} = nM - P$

Over a long term this figure is startling — at high rates and 30 years it can exceed the amount borrowed. That is not a hidden fee; it is $360$ months of interest on a balance that takes decades to fall.

Solving for the rate

There is no closed form for $r$ given $P$, $M$ and $n$. It is found numerically, by trying rates until the computed payment matches the actual one. The APR on a loan with fees is found the same way, using the net amount you actually received as $P$.

Ratios lenders look at

$\text{LTV} = \frac{\text{loan}}{\text{value}}, \qquad \text{DTI} = \frac{\text{monthly debt payments}}{\text{gross monthly income}}$

These are arithmetic; the thresholds applied to them are lender and programme policy, they change, and we do not publish them.

• Using the annual rate as the monthly rate: divide by 12 first. A 6% loan accrues $0.5\%$ a month.
• Multiplying principal $\times$ rate $\times$ years on an amortizing loan: that is simple interest and it badly overstates the cost, because the balance falls each month.
• Mixing 360- and 365-day conventions: on a large balance the difference in a per-diem quote is real money. Use the divisor your contract specifies.
• Assuming an interest-only payment reduces the debt: it does not. The balance is unchanged until the loan converts to amortizing or you pay extra.
• Forgetting escrow: a mortgage payment usually bundles taxes and insurance. The formula above returns principal and interest only.
• Confusing rate with APR: APR includes certain financing costs, so it usually sits above the note rate. Compute the payment from the rate the contract uses.
• Reading a DTI or LTV result as an approval: those are ratios, not decisions. Only a lender can tell you what qualifies.