Read the guide

P/Y and C/Y: payments and compounding are different inputs

Convert a quoted nominal rate into a payment-period rate and avoid treating years as the number of payments.

Payment frequency tells you how often cash moves. Compounding frequency tells you how the quoted nominal interest rate accumulates. Those two frequencies can match, but they are not interchangeable definitions.

For an exercise, write the annual rate convention in words before entering a percentage. '6% nominal, compounded semiannually' and '6% effective annually' are different starting points.

Convert before using a payment formula

Let j be the nominal annual rate as a decimal, C the number of compounding periods per year, and P the payments per year. An equivalent payment-period rate is (1 + j/C) raised to C/P, minus 1.

For 6% nominal interest compounded twice per year and twelve payments per year, that gives (1.03)^(1/6) − 1, or approximately 0.493862% per month. Simply dividing 6% by twelve would describe monthly compounding instead.

Keep N on the payment timeline

A three-year schedule with monthly payments has 36 payments when the schedule covers three full years in that pattern. Entering N = 3 while using a monthly rate changes the model to three monthly periods.

As an arithmetic comparison, a 10,000 present value repaid by twelve END payments at the semiannual-compounding example rate gives a payment magnitude of roughly 860.33. The figure is illustrative and excludes fees and date-specific conventions.

Record the annual-rate type too

An effective annual rate e converts to a payment-period rate using (1 + e)^(1/P) − 1. It should not be placed into a nominal-rate formula and divided by C again.

Yieldra keeps P/Y and C/Y separate. When checking textbook keystrokes or another calculator, verify those worksheet settings rather than assuming their defaults match. The correct settings are part of the problem, not hidden housekeeping.

  • Write nominal or effective next to the quoted rate.
  • Count payments separately from years.
  • Check whether the problem uses regular equal periods.

Questions, answered

Is dividing an annual rate by twelve always wrong?

It is appropriate for a nominal annual rate compounded monthly in a monthly-period model. It is not a universal conversion for every quoted annual rate.

Can this method price irregular dated cash flows?

Not directly. Unequal dates need a model with explicit dates or appropriate day-count conventions.

Sources & method

Reviewed:

Keep going in Yieldra

Free TVM keys and a result card showing balance, interest and total interest · Visible N, I/Y, PV, PMT and FV registers, with separate P/Y and C/Y settings · Offline calculations; Pro adds worksheets, extra payments, saved problems and PDF/CSV export

Get the iPhone app

Keep exploring