Bond price and YTM on a financial calculator

For CFA Chartered Financial Analyst (CFA) Level I problems where the bond settles on a coupon date, both the BA II Plus and the HP 12C handle bond price and Yield to Maturity (YTM) through their Time Value of Money (TVM) keys. The five TVM registers (N, I/Y or i, PV, PMT, FV) map cleanly onto a coupon bond.

This page walks four worked examples through the TVM-routed path on both calculators. The dedicated bond worksheets (2nd BOND on the BA II Plus, f PRICE and f YTM on the HP 12C) handle off-coupon-date settlement and day-count conventions; for the on-coupon-date cases that dominate the curriculum, TVM is faster.

Try the BA II Plus calculator

Try the HP 12C calculator

TVM mapping for a coupon bond

Three rules apply to every bond problem:

1. Periodic, not annual. For a semiannual coupon bond, halve the annual YTM before storing it in I/Y or i.
2. Sign convention. PV is negative (the buyer parts with the price). PMT and FV are positive (the buyer receives coupons and redemption).
3. Clear before starting. Always clear TVM (2nd CLR TVM on the BA II Plus, f FIN on the HP 12C) so prior register values do not bleed in.

Worked example 1: annual-coupon bond price

Problem. A 10-year, 5 percent annual-coupon bond with a 1,000 face value trades to yield 6 percent. Compute the price.

BA II Plus:

1. 2nd then CLR TVM
2. 10 then N
3. 6 then I/Y
4. 50 then PMT (coupon = 5 percent × 1,000 = 50, annual)
5. 1000 then FV
6. CPT then PV

Expected PV: -926.3991. The buyer pays 926.40 rounded.

HP 12C:

1. f FIN
2. 10 then n
3. 6 then i
4. 50 then PMT
5. 1000 then FV
6. PV

Expected PV: -926.3991. Same answer to four decimals, because the two engines share the canonical TVM solver.

Replay on the BA II Plus | Replay on the HP 12C

Worked example 2: semiannual-coupon bond price

Problem. A 5-year, 6 percent annual coupon (paid semiannually) on a 1,000 face value trades to yield 7 percent annual YTM. Compute the price.

Map to TVM:

• N = 5 × 2 = 10 periods
• I/Y or i = 7 / 2 = 3.5 percent per period
• PMT = (6 percent × 1,000) / 2 = 30 per period
• FV = 1,000

BA II Plus: 2nd CLR TVM, 10 N, 3.5 I/Y, 30 PMT, 1000 FV, CPT PV.

HP 12C: f FIN, 10 n, 3.5 i, 30 PMT, 1000 FV, PV.

Expected PV: -958.4170. Buyer pays 958.42 rounded.

Worked example 3: solve for YTM

Problem. A 5-year, 6 percent annual coupon (paid semiannually) on a 1,000 face value currently trades at 980. Compute the annual YTM.

Map to TVM:

• N = 10
• PV = -980 (the buyer paid 980)
• PMT = 30
• FV = 1,000

Solve for I/Y (per period).

BA II Plus: 2nd CLR TVM, 10 N, 980 +/- PV, 30 PMT, 1000 FV, CPT I/Y. Expected periodic yield: 3.2373... percent. Multiply by 2 for the annual YTM: 6.4746 percent.

HP 12C: f FIN, 10 n, 980 CHS PV, 30 PMT, 1000 FV, i. Expected periodic yield: 3.2373... percent. Multiply by 2: 6.4746 percent.

The CFA convention reports YTM as the bond-equivalent yield (twice the periodic yield) for semiannual coupon bonds. Both calculators return the periodic yield; the candidate doubles it.

Worked example 4: zero-coupon bond

Problem. A 10-year zero-coupon bond with a 1,000 face value trades to yield 5 percent. Compute the price.

Map to TVM:

• N = 10
• I/Y or i = 5
• PMT = 0
• FV = 1,000

BA II Plus: 2nd CLR TVM, 10 N, 5 I/Y, 0 PMT, 1000 FV, CPT PV.

HP 12C: f FIN, 10 n, 5 i, 0 PMT, 1000 FV, PV.

Expected PV: -613.9133. Buyer pays 613.91 rounded.

When the TVM path is not enough

For settlement on a coupon date, the TVM path is exact. For settlement between coupon dates, accrued interest and a day-count basis matter, and the dedicated bond worksheet on each device handles them:

• BA II Plus: 2nd BOND opens a worksheet with settlement date (SDT), redemption date (RDT), coupon rate (CPN), redemption value (RV), day-count basis (ACT/ACT, 30/360, ACT/360, ACT/365), and yield (YLD) fields.
• HP 12C: f PRICE and f YTM use day inputs from the date keys.

For CFA Level I curriculums, off-coupon-date settlement is rare. The candidate-facing exam questions almost always settle on a coupon date, and the TVM path on this page is the cleaner workflow.

Common mistakes on bond problems

1. Annual rate stored as periodic. Halving the annual YTM is the most common omission. The semiannual periodic rate is half the annual YTM for a semiannual coupon bond. Forgetting the halve gives a price that is too low (the discount is too aggressive).
2. Sign convention. Same as the HP 12C sign convention and the BA II Plus M4 rule. PV is negative; PMT and FV are positive.
3. Stale TVM registers. The previous problem's PV is still loaded. Clear before every bond problem.
4. N counted in years, not in coupon periods. For semiannual coupons, N is twice the years to maturity.

Charterly's calculator catches the stale-register case under M3 (BA II Plus) and H3 (HP 12C). The other three are workflow habits this page teaches.

Related pages

• BA II Plus CFA guide section 4 covers a bond worked example as part of the broader walkthrough.
• HP 12C CFA guide section 4 mirrors it on HP.
• The twelve CFA calculator mistakes for the named-rule list across both devices.

Frequently asked questions

Does this page cover bond duration and convexity? No. Duration and convexity have their own keystroke path on the BA II Plus Professional and live as derived values on the standard models. They are tracked separately on the advanced calculators surface.

Can I price a callable bond on the TVM path? For yield-to-call problems, yes. Set N to the call date in periods, PMT to the periodic coupon, FV to the call price, and solve for I/Y (then double for semiannual coupon convention). The TVM path treats the call as a standard redemption.

Why does the BA II Plus return a negative PV? Sign convention. The negative sign means the buyer parts with the value. The price the buyer pays is the absolute value. Display the rounded positive number as the answer.

Does Charterly support the bond worksheet for off-coupon-date settlement? The current calculator routes through TVM for the on-coupon-date workflow. Full bond worksheet with day-count basis is on the roadmap. The TVM path covers the majority of Level I curriculum.