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BA II PLUS: different payment and compounding frequencies

Payment intervals and compounding intervals can differ; the equivalent factor connects them.

Omni Finance AcademyBy Omni Finance Academy
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State the synthetic payment pattern

Suppose the modeled cash receipts are 100 at the end of each month for twenty-four months. The annual quotation is nominal 6% compounded quarterly. Payments are monthly, while the quotation’s compounding is quarterly.

Derive the equivalent monthly rate

One quarter has gross factor 1.015. Three monthly gross factors must multiply to that factor, so the monthly rate is 1.015^(1/3) − 1, approximately 0.497521%. It is not exactly 6%/12.

Enter distinct worksheet frequencies

Clear prior TVM values and select END in the timing worksheet to match the end-month receipts. Then enter the frequency state below.

  1. Choose monthly payments2ndP/Y12ENTER

    P/Y becomes twelve and may also change C/Y.

  2. Restore the required quarterly compounding↓4ENTER2ndQUIT

    C/Y is four, while P/Y remains twelve.

  3. Enter known TVM quantities and compute24N6I/Y100PMT0FVCPTPV

    The receiver-perspective expected PV is −2,256.96926; a zero FV and cleared prior values are part of the state.

Reconcile with a separate periodic calculation

The independent magnitude is 100 × [1 − (1 + r)^−24]/r with the equivalent monthly r. It gives 2,256.96926. The annual-rate number belongs to the device state, while the monthly rate belongs to this independent formula; do not interchange the two inputs.

Further references