How to Calculate Macaulay and Modified Duration on a BA II Plus

In this tutorial

• Macaulay vs modified duration in one sentence each
• Opening and clearing the BOND worksheet
• Entering the dates, coupon, redemption value and yield
• Example 1: a 5-year 6% bond at 7% YTM
• Example 2: a 10-year 8% bond at 6% YTM
• Converting DUR to modified duration by hand
• Common mistakes and date-format traps

If the problem instead hands you a price and asks for the yield, the YTM tutorial covers that direction, and the bond pricing tutorial covers the price itself.

Macaulay vs modified duration in one sentence each

• Macaulay duration — the weighted average time (in years) until each cash flow is received, weighted by its present value. It answers "how long, on average, do I wait to get my money back from this bond?"
• Modified duration — the approximate percentage change in price for a 1% change in yield. It is Macaulay duration divided by (1 + yield per period).

The BA II Plus BOND worksheet reports Macaulay duration as DUR. It does not report modified duration directly — the conversion is a single division you do on the keypad.

Opening and clearing the BOND worksheet

1. Press [2nd] then [9] (BOND).
2. Press [2nd] then [CLR WORK] to reset the worksheet.
3. You will see SDT= with a date. Enter the settlement date in MM.DDYY format (for example 1.1506 means January 15, 2026) and press [ENTER].

The worksheet walks down through CPN (annual coupon rate in percent), RDT (redemption date), RV (redemption value, default 100), a day-count setting, 2/Y (coupon payments per year) and YLD (yield in percent).

Example 1: a 5-year 6% bond at 7% YTM

A bond matures January 15, 2031, pays a 6% annual coupon semiannually, and settles on January 15, 2026 at a yield to maturity of 7%. Face value $1,000.

1. Press [2nd] then [9], then [2nd] then [CLR WORK].
2. At SDT=, enter 1.1506, press [ENTER].
3. At CPN=, enter 6, press [ENTER].
4. At RDT=, enter 1.1531, press [ENTER].
5. At RV=, keep 100 (enter 100 and [ENTER] to be safe).
6. Confirm the day-count setting (default ACT is fine for most problems).
7. At 2/Y=, enter 2, press [ENTER].
8. At YLD=, enter 7, press [ENTER].
9. Press ↑ or scroll back to PRI and press [CPT] to see the price: 95.84 (that is 95.84% of face value, or $958.40).
10. Scroll down past AI (accrued interest, 0 here because settlement falls on a coupon date) to DUR=: read 4.38 — the Macaulay duration in years.

Hand check of the relationship: modified duration = 4.38 ÷ (1 + 7% ÷ 2) = 4.38 ÷ 1.035 = 4.23. So a 1% (100 bp) rise in yield should lower this bond's price by roughly 4.23%.

Example 2: a 10-year 8% bond at 6% YTM

A longer, higher-coupon bond: matures January 15, 2036, pays 8% semiannually, settles January 15, 2026 at a 6% YTM.

1. Clear the worksheet: [2nd] then [9], [2nd] then [CLR WORK].
2. Enter SDT = 1.1506, CPN = 8, RDT = 1.1536, RV = 100, 2/Y = 2, YLD = 6 — each followed by [ENTER].
3. Press [CPT] at PRI: the price is 114.88 ($1,148.80 per $1,000) — a premium bond, matching the earlier bond pricing example.
4. Scroll to DUR=: read 7.29 — the Macaulay duration in years.

Modified duration = 7.29 ÷ (1 + 6% ÷ 2) = 7.29 ÷ 1.03 = 7.08. The longer maturity dominates: this bond is far more rate-sensitive than the 5-year bond in Example 1, despite the higher coupon.

Converting DUR to modified duration by hand

1. Read DUR from the BOND worksheet.
2. Press ÷, type 1 + (YLD ÷ coupons per year), press ENTER.

For Example 1: 4.38 ÷ 1 + 7 ÷ 2 = ENTER → 4.23. Exam questions almost always ask for modified duration, so practice the division until it is automatic.

Common mistakes and date-format traps

• Date format confusion. SDT uses MM.DDYY, not month/day/year ordering as you write it — 1.1506 is January 15, 2026. Reading "06.1.15" style dates as MM.DDYY causes year errors.
• Two-digit years. A redemption date in 2031 must be entered as 1.1531. The worksheet's two-digit year rolls over near the century boundary; verify the date after [ENTER].
• Settlement after redemption. If SDT is later than RDT, the calculator refuses or produces nonsense — check both dates before computing.
• RV = 100 vs 1,000. The worksheet prices per 100 of face value by default. Leaving RV at 100 is correct for percentage outputs; typing 1000 changes the price display scale but not duration.
• Day-count setting. The default ACT is right for most exam problems; ACT/360 and 30/360 are available with [2nd] then [SET]. Changing it changes accrued interest on non-coupon dates.
• Reading DUR as modified duration. They differ by about 3–4% at typical yields. Exam answers in the choices are close enough that this mistake is fatal — do the division.
• Forgetting CLR WORK. Leftover coupon or yield values quietly produce a duration for the wrong bond.

Related tutorials

Duration builds on the price from the bond pricing tutorial and inverts the yield logic of the YTM tutorial. The discounting mechanics come from future value and present value, and the basics tutorial covers the key layout for every worksheet on the calculator.

References

• Texas Instruments — BA II PLUS Guidebook (official user manual, BOND worksheet)
• Investopedia — Macaulay Duration: Definition, Formula, Example, and How It Works
• Investopedia — Modified Duration: Meaning, Formula, Examples
• Corporate Finance Institute — Duration