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How to convert a nominal rate to an effective annual rate

A rate compounded monthly earns more than its headline number. Growing $100 for a year shows exactly how much more.

Problem

A savings account pays 6% a year, compounded monthly. What is the effective annual rate (APY)?

Keystrokes

  1. fFINx≷y
    0.00

    Start clean.

  2. 12n
    12.00

    Twelve compounding periods in the year.

  3. 6ENTER12÷i
    0.50

    The rate per period.

  4. 100CHSPV
    −100.00

    Invest $100.

  5. FV
    106.17

    What it grows to in a year.

  6. 100−
    6.17

    The growth on $100, which is the effective rate in percent.

Answer

6% compounded monthly is an effective 6.17% a year.

Why it works

Using $100 makes the dollar gain equal the percentage rate. The same steps work for any compounding: daily compounding is 365n and the rate divided by 365.

Questions

How do I go the other way?

Key 12 n, 100 CHS PV, and 100 plus the effective rate in FV, then press i and multiply by 12.

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