How this calculator works
When interest compounds more often or less often than you pay, the payment is not simply the nominal rate divided by the number of payments. The calculator converts the nominal annual rate into an equivalent rate for each payment period using the stated compounding interval, then amortises the loan at that rate. Continuous compounding is the limiting case where interest is added without pause. The effective annual rate shows what the same loan would charge over one year if interest were compounded once, which makes offers with different intervals comparable.
Formula
With c compounding periods a year and k payments a year, the rate per payment is i = (1 + r/c)^(c/k) - 1, and the effective annual rate is (1 + r/c)^c - 1. For continuous compounding, i = e^(r/k) - 1 and the effective annual rate is e^r - 1. Payment A = P × i / (1 - (1 + i)^(-n)) with n = term × k. Total interest = n × A - P.
Worked example
Borrowing $25,000 at a nominal 6% for 5 years with monthly payments costs $483.32 a month when interest compounds monthly, for $3,999.20 of interest and an effective annual rate of 6.1678%. If the same nominal rate compounds semi-annually, the periodic rate falls to 0.4939% a month, the payment drops to $482.46, interest is $3,947.86 and the effective annual rate becomes 6.09%. Less frequent compounding costs less at the same nominal rate.
Advertisement
Frequently asked questions
Is a nominal rate the same as an effective rate?
No. A nominal rate ignores how often interest is added; an effective annual rate converts the same terms into one year of compounding. Two loans with the same nominal rate can have different effective rates if their compounding intervals differ.
Which compounding interval should I choose?
Use the interval stated in your agreement. Canadian mortgages typically compound semi-annually, many personal loans monthly, and credit cards daily. Choosing the wrong interval changes the payment.
What does continuous compounding mean?
It is a mathematical limit in which interest is added constantly rather than at fixed intervals. It appears in some finance textbooks and contracts; for ordinary consumer loans the difference from daily compounding is small.
Why does a higher compounding frequency cost more?
Interest compounds on interest, so the more often it is added, the faster the effective balance grows at the same nominal rate. The effective annual rate captures the size of that effect.