The Interest Conversion worksheet

The Interest Conversion worksheet turns a nominal interest rate into an effective one, or the effective rate back into the nominal, given how often interest compounds in a year. It is one of the worksheets in Financial mode. From the Financial calculator, use the Calculator ⇄ Worksheets toggle to switch to the worksheet list, then pick Interest Conv; the worksheet expands into the workspace. For the whole set of worksheets and how you move between them, see the Financial calculator.

Reach for this worksheet whenever two rates are quoted on different compounding frequencies and you need to compare them fairly. A savings account advertised at "6% compounded monthly" and a bond quoted at "6.1% compounded annually" cannot be compared on their headline numbers alone — you have to put both on the same footing first. That common footing is the effective annual rate, and this worksheet is how you compute it.

The worksheet has two regions: a form on the left, where you enter the rates and the compounding frequency and choose which way to solve; and a result card on the right, which appears once you compute and shows the answer in large type. Below the form sits the Compute button, and any input problem is reported as a short message beneath it.

The three quantities

Every interest conversion is a relationship between three values. The worksheet gives each one a field, labelled with a short key on the left and a description beneath the box.

The nominal and effective fields hold percents, so you type 12 for twelve percent, not 0.12. Rates are shown to three decimal places (for example 12.683).

Why the two rates differ

Nominal and effective rates describe the same account, but they answer different questions, and they only agree when interest compounds exactly once a year.

The nominal rate is a simple yearly label. "12% compounded monthly" means the year is split into twelve equal slices and one-twelfth of the nominal rate — 1% — is applied at the end of each slice. The catch is that each month's interest is itself added to the balance, so the next month's 1% is charged on a slightly larger amount. Interest earns interest. By the end of the year the balance has grown by more than the flat 12% the nominal rate seems to promise.

The effective rate is that true, all-in growth over one year: the single annual rate that would leave you in exactly the same place. Because compounding adds interest on top of interest, the effective rate is always higher than the nominal rate whenever interest compounds more than once a year — and the more frequently it compounds, the wider the gap. When C/Y is 1, there is no intra-year compounding to account for, and the two rates are equal.

This is why the effective rate is the fair basis for comparison. Two offers with different nominal rates and different compounding frequencies become directly comparable the moment you convert both to their effective annual rates.

Converting in either direction

A segmented control in the form sets the direction of the conversion:

• NOM → EFF — you know the nominal rate; solve for the effective rate. This is the default.
• EFF → NOM — you know the effective rate; solve for the nominal rate needed to produce it at the chosen compounding frequency.

Pick a direction, fill in the two fields it needs (the source rate and C/Y), and press Compute. The field you are solving for is filled in with the answer and marked with a small SOLVED tag, and the result card on the right shows the same value in large type, labelled EFFECTIVE RATE or NOMINAL RATE, with the compounding frequency repeated underneath.

If a required entry is missing or invalid, the worksheet tells you what it needs rather than computing a wrong answer. Leaving the compounding field blank or zero prompts you to enter the compounding periods per year (positive); leaving the source rate blank prompts you to enter the nominal (or effective) rate for the direction you chose.

Worked example: a nominal rate compounded monthly

A credit card is advertised at a nominal annual rate of 12%, compounded monthly. What is the effective annual rate you actually pay?

1. Switch to the worksheet list and select Interest Conv.
2. Leave the direction on NOM → EFF.
3. In NOM, enter 12.
4. In C/Y, enter 12 (twelve compounding periods a year — monthly).
5. Press Compute.

The EFF field fills in with 12.683 and shows its SOLVED tag, and the result card reads EFFECTIVE RATE, 12.683 %, with 12 compounding periods / year beneath it. The card confirms what the reasoning above predicted: twelve monthly slices of 1%, each compounding on the last, come to about 12.683% over the year — noticeably more than the flat 12% headline.

To run the conversion the other way, switch the direction to EFF → NOM, type 12.683 into EFF, keep C/Y at 12, and press Compute; the NOM field returns to 12.000.

Related chapters

• The Financial calculator — the worksheet list, the tape, and the calculator keypad.
• Time value of money — the N, I/Y, PV, PMT, FV worksheet, where the effective rate you compute here feeds a loan or investment calculation.