How do I find the interest rate on a loan?

Enter the amount financed, the payment and the number of payments. The calculator solves for the rate that equates the price to the present value of the payments.

Is "no interest" financing really free?

Only if the total of payments equals the cash price. If there is a cash discount you forgo, the plan carries hidden interest.

Why is the annual rate higher than 12 times the monthly?

Because it compounds: (1 + monthly)^12 − 1. A 2% monthly rate is about 27% a year, not 24%.

Should I pay cash or finance?

Compare the implied rate with what your money would earn. If the rate is higher, paying cash saves more than investing would.

Finance

Interest Rate Calculator

"No interest" is not always true. Enter the cash price, the payment and the number of payments, and the calculator finds the interest rate actually built into the plan — monthly and annually.

Your numbers

Result

Monthly rate

2.92%

Effective annual rate

41.3%

Total interest: $200.00
Total of payments: $1,200.00

The rate hidden in the payments
Item	Value
Total of payments	$1200.00
Interest paid	$200.00
Monthly rate	2.92%
Effective annual rate	41.30%

How the rate is found

There is no direct formula for the rate, so the calculator solves for the i that makes the cash price equal the present value of the payments: price = payment × (1 − (1 + i)^−n) ÷ i. It searches numerically (bisection). If the total of payments equals the cash price, the rate is zero — genuinely interest-free.

A cash discount is hidden interest

When a store offers a cash discount, a "no interest" installment plan really does carry interest — you give up the discount by financing. Always compare the cash price against the total of the payments. If the implied rate beats what your money would earn, pay cash.

Monthly vs. annual

A small monthly rate compounds into a much larger annual one: the effective annual rate is (1 + i)^12 − 1, so 2% a month is about 27% a year, not 24%. This is why comparing offers on the annual rate — not the monthly — keeps you honest.

Informational and educational result. Not a substitute for professional advice.

Frequently asked questions

Sources

Financial math — internal rate of return (amortization)

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