How to Read
Legend for this calculator guide
N = a key as printed; 2nd P/Y = BA II Plus second function (label above the key); f / g = HP 12C gold / blue shift; display results appear as 0.00. Numbers you type are shown plainly (e.g. 1000000).
Steel boxesKeys & methods — Setting / Keystrokes / Why tables
Green boxesWorked examples on both calculators
Orange boxesExam traps that silently change answers
Blue-grey boxesReference facts and formulas
Source note: formulas and several examples come from the GARP/Schweser Part I books (reading cited where used). Keystroke sequences follow the Texas Instruments and HP owner’s manuals — practise each one on your own calculator.
Chapter 01
1. Permitted Calculators & Setup
What GARP allows, the settings to fix once, and how to clear before every question.
Calculators permitted in the FRM exam (GARP exam policy)
| Brand / rule | Detail |
|---|---|
| Texas Instruments | BA II Plus, including the BA II Plus Professional. |
| Hewlett Packard | HP 12C (including 12C Platinum, 12C Platinum 25th Anniversary Edition, 12C 30th Anniversary Edition and 12C Prestige), HP 10B II, HP 10BII+, HP 20B. |
| Rule | Any other calculator at any time ⇒ the exam is not graded. No exceptions. Bring fresh batteries. Always re-check the current list on garp.org before your exam. |
| Which to choose? | BA II Plus: algebraic entry, most Indian coaching material uses it, has bond/date/amortisation worksheets. HP 12C: RPN entry, very fast once learnt, built-in PRICE/YTM and dates. This guide covers both. |
1.1 BA II Plus — one-time setup (do this first)
| Setting | Keystrokes | Why |
|---|---|---|
| Reset to factory defaults | 2nd RESET ENTER CE/C | Clears everything. After a reset P/Y = 12, DEC = 2, method = Chn. |
| Payments per year = 1 | 2nd P/Y 1 ENTER 2nd QUIT | Then I/Y = rate per period. C/Y changes to 1 automatically. |
| 4 decimal places | 2nd FORMAT 4 ENTER 2nd QUIT | Shows answers such as 0.0769 or 7.0728. Use 9 for floating. |
| Algebraic (AOS) order | 2nd FORMAT ↓ ↓ ↓ ↓ (shows Chn) 2nd SET (shows AOS) 2nd QUIT | With Chn, 2 + 3 × 4 = 20; with AOS, = 14 (normal maths). AOS recommended. |
| End-mode payments | 2nd BGN (if BGN shows: 2nd SET) 2nd QUIT | “BGN” in the display = annuity due. Normal problems need END (no indicator). |
1.2 HP 12C — one-time setup
| Setting | Keystrokes | Why |
|---|---|---|
| 4 decimal places | f 4 | Display only; the HP always keeps full precision internally. |
| End-mode payments | g END (blue label on 8) | “BEGIN” in the display = annuity due (g BEG on 7). |
| Date format | g M.DY (on 5) | Dates keyed as MM.DDYYYY (g D.MY for DD.MMYYYY — “D.MY” shows). This guide uses M.DY. |
| No P/Y setting | — | i is always the rate per period and n the number of periods. Use g 12× / g 12÷ for monthly problems. |
| Change sign | CHS | Not the − key. Enter outflows as negative. |
Clearing — do it before every question
- BA: TVM registers2nd CLR TVM (above FV) — sets N, I/Y, PV, PMT, FV to 0. CE/C alone does not clear them.
- BA: a worksheetOpen it (e.g. CF, 2nd DATA, 2nd BOND) then 2nd CLR WORK (above CE/C).
- BA: leave a worksheet2nd QUIT (above CPT).
- HP: financial registersf FIN (gold, above x≷y) — clears n, i, PV, PMT, FV.
- HP: all registersf REG (above CLx) — clears financial, statistics, memory and cash flows. Use before NPV/IRR.
- HP: statisticsf Σ (above SST) — clears the statistics registers (and the stack).
- HP: display onlyCLx.
Chapter 02
2. HP 12C: How RPN Works
Reverse Polish Notation in five minutes — no equals key, no brackets.
2.1 The stack and the ENTER key
The HP holds numbers in a four-level stack (X, Y, Z, T). The display is X. ENTER copies X into Y so you can type the next number. An operation (+ − × ÷ yx) combines Y and X and puts the result in X. One-number functions (g LN, g ex, g √x, g x², 1/x) act on X only.
Algebraic: (2 + 3) × 4 ⇔ RPN: 2 ENTER 3 + 4 × ⇒ 20.0000
Rule of thumb: type the first number, press ENTER, type the second, press the operation. After an operation the answer is ready for the next step — no need to press ENTER again (a new number automatically pushes it up to Y). x≷y swaps X and Y; R↓ rolls the stack; g LSTx recalls the last X.
Worked example — RPN warm-up
50/45 then ln50 ENTER 45 ÷ g LN ⇒ 0.1054
1.03²1.03 ENTER 2 yx ⇒ 1.0609
√0.250.25 g √x ⇒ 0.5000
(1.65 × 0.0125) − 0.001881.65 ENTER 0.0125 × 0.00188 − ⇒ 0.0187
Chapter 03
3. Maths Keys & FRM Formulas
Exponentials, logs, powers, factorials — and the exam formulas that use them.
3.1 Where the maths functions are
| Function | BA II Plus | HP 12C |
|---|---|---|
| ex | 2nd ex (above LN) | g ex (on 1/x) |
| ln x | LN | g LN (on %T) |
| x², √x | x², √x | g x² (on ×), g √x (on yx) |
| yx | y yx x = | y ENTER x yx |
| 1/x | 1/x | 1/x |
| n! | n 2nd x! | n g n! (on 3) |
| nCr (combinations) | n 2nd nCr r = | n! / [r! (n − r)!] by hand |
| Change sign | +/− | CHS |
| Previous answer | 2nd ANS | automatic (stack) |
Neither calculator gives the cumulative normal N(d) — the exam provides a z-table or the values.
BA functions such as LN, x², √x act immediately on the number in the display.
Worked example — FRM formulas on the calculator (BA II Plus in AOS mode)
Normal VaR (VRM Ch. 1): (1.65 × 0.0125 − 0.00188) × 100m1.65 × 0.0125 − 0.00188 = × 100000000 = ⇒ 1,874,500.0000
EWMA σ (VRM Ch. 3): √[0.94(0.01²) + 0.06(0.02²)]0.94 × 0.01 x² + 0.06 × 0.02 x² = √x ⇒ 0.0109 (1.086%)
Forward 100e0.05×0.5 (FMP)0.05 × 0.5 = 2nd ex × 100 = ⇒ 102.5315
Hazard PD 1 − e−0.02×4 (VRM Ch. 4)0.08 +/− 2nd ex +/− + 1 = ⇒ 0.0769
BSM d1 (VRM Ch. 15): S=50, X=45, r=5%, σ=12%, T=0.2550 ÷ 45 = LN + ( 0.05 + 0.12 x² ÷ 2 ) × 0.25 = ÷ ( 0.12 × 0.25 √x ) = ⇒ 1.9943
Binomial u = e0.14√1; πu = (e0.04 − 1/u) / (u − 1/u)0.14 2nd ex STO 1 ⇒ 1.1503; ( 0.04 2nd ex − RCL 1 1/x ) ÷ ( RCL 1 − RCL 1 1/x ) = ⇒ 0.6103
Poisson P(3) = e−2 23 / 3! (VRM Ch. 7)2 +/− 2nd ex × 2 yx 3 ÷ 3 2nd x! = ⇒ 0.1804
Combinations 10C310 2nd nCr 3 = ⇒ 120.0000
Worked example — The same formulas on the HP 12C (RPN)
Normal VaR1.65 ENTER 0.0125 × 0.00188 − 100000000 × ⇒ 1,874,500.000
EWMA0.94 ENTER 0.01 g x² × 0.06 ENTER 0.02 g x² × + g √x ⇒ 0.0109
Forward 100e0.025100 ENTER 0.05 ENTER 0.5 × g ex × ⇒ 102.5315
Hazard PD1 ENTER 0.08 CHS g ex − ⇒ 0.0769
BSM d150 ENTER 45 ÷ g LN 0.12 ENTER × 2 ÷ 0.05 + 0.25 × + 0.12 ENTER 0.25 g √x × ÷ ⇒ 1.9943
Binomial u, πu0.14 g ex STO 1; 0.04 g ex RCL 1 1/x − RCL 1 RCL 1 1/x − ÷ ⇒ 0.6103
Poisson P(3)2 CHS g ex 2 ENTER 3 yx × 3 g n! ÷ ⇒ 0.1804
Combinations 10C310 g n! 3 g n! ÷ 7 g n! ÷ ⇒ 120.0000
Chapter 04
4. Time Value of Money (TVM)
The five TVM keys, sign convention, annuities, annuity due, monthly problems, perpetuities.
4.1 The five keys
| Variable | BA II Plus | HP 12C | Meaning |
|---|---|---|---|
| Number of periods | N | n | Years × payments per year |
| Rate per period | I/Y | i | In % (8, not 0.08). With P/Y = 1 on the BA, key the periodic rate |
| Present value | PV | PV | Today’s amount |
| Payment | PMT | PMT | Level amount each period (coupon, instalment) |
| Future value | FV | FV | Amount at the end (face value) |
| Solve | CPT then the key | just press the key | HP has no CPT key |
PV = PMT/i × [1 − 1/(1+i)N] + FV/(1+i)N
Sign convention: money you pay out is negative, money you receive is positive. PV and FV (or PV and PMT) must have opposite signs, otherwise both calculators show Error 5 (no solution). Enter known values in any order; enter 0 for anything not used (or clear first).
Worked example — Future value and present value
FV: INR 1,00,000 at 8% for 5 years
BA: 2nd CLR TVM 5 N 8 I/Y 100000 +/− PV 0 PMT CPT FV ⇒ 146,932.8077
HP: f FIN 5 n 8 i 100000 CHS PV FV ⇒ 146,932.8077
HP: f FIN 5 n 8 i 100000 CHS PV FV ⇒ 146,932.8077
PV: INR 5,00,000 needed in 10 years at 7%
BA: 10 N 7 I/Y 500000 FV 0 PMT CPT PV ⇒ −254,174.6461
HP: 10 n 7 i 500000 FV 0 PMT PV ⇒ −254,174.6461
HP: 10 n 7 i 500000 FV 0 PMT PV ⇒ −254,174.6461
Monthly: PV of 1,000 in 2 years at 3% compounded monthly (VRM Ch. 10 quiz)
BA: 24 N 0.25 I/Y 1000 FV 0 PMT CPT PV ⇒ −941.8351
HP: 2 g 12× 3 g 12÷ 1000 FV 0 PMT PV ⇒ −941.8351
HP: 2 g 12× 3 g 12÷ 1000 FV 0 PMT PV ⇒ −941.8351
Worked example — Annuity, annuity due and perpetuity
Annuity: 100 a year for 10 years at 10% (VRM Ch. 11)
BA: 10 N 10 I/Y 100 PMT 0 FV CPT PV ⇒ −614.4567
HP: 10 n 10 i 100 PMT 0 FV PV
HP: 10 n 10 i 100 PMT 0 FV PV
Annuity due (payments at the start)
BA: 2nd BGN 2nd SET 2nd QUIT then CPT PV ⇒ −675.9024 (= 614.4567 × 1.10).
HP: g BEG PV. Switch back to END afterwards!
Perpetuity: 1,000 a year at 10%
No TVM key needed: 1,000 / 0.10 = 10,000. (TVM trick: N = 999 gives almost the same.)
EXAM TRAP: BA II Plus after a reset has P/Y = 12: keying 8 in I/Y then means 8%/12 per period and every answer is wrong. Set P/Y = 1 and always key the periodic rate yourself.
EXAM TRAP: Leaving BGN on from a previous question silently changes every TVM answer.
EXAM TRAP: A leftover PMT or FV from the last question corrupts the next one — clear TVM each time.
Chapter 05
5. Interest-Rate Conversion
Nominal vs. effective, periodic, and continuously compounded rates (VRM Ch. 10; FMP).
5.1 Formulas and keys
EAR = (1 + Rm/m)m − 1 |
Rc = m ln(1 + Rm/m) |
Rm = m (eRc/m − 1)
BA II Plus ICONV worksheet:
2nd ICONV → NOM= key rate ENTER ↓ ↓ C/Y= key m ENTER ↑ EFF= CPT.
(Reverse: enter EFF and C/Y, go to NOM, CPT.)
HP 12C: no worksheet — use the formula, or the TVM trick: m n Rm/m i 100 CHS PV 0 PMT FV gives 100 × (1 + EAR).
HP 12C: no worksheet — use the formula, or the TVM trick: m n Rm/m i 100 CHS PV 0 PMT FV gives 100 × (1 + EAR).
Worked example — Converting 6% semiannual (Schweser VRM Reading 56)
Effective annual rate
BA: 2nd ICONV 6 ENTER ↓ ↓ 2 ENTER ↑ CPT ⇒ EFF= 6.0900.
HP: 1.03 ENTER 2 yx 1 − 100 × ⇒ 6.0900
Equivalent monthly rate
BA: keep EFF = 6.09; ↓ 12 ENTER ↑ ↑ NOM= CPT ⇒ 5.9263.
HP: 1.03 ENTER 6 1/x yx 1 − 12 × ⇒ 0.0593
Continuous equivalent 2 ln 1.03
BA: 1.03 LN × 2 = ⇒ 0.0591.
HP: 1.03 g LN 2 × ⇒ 0.0591 (5.91%)
5% continuous → semiannual
BA: 0.025 2nd ex − 1 = × 2 = ⇒ 0.0506.
HP: 0.025 g ex 1 − 2 × ⇒ 0.0506
12% monthly → EAR
BA: 2nd ICONV 12 ENTER ↓ ↓ 12 ENTER ↑ CPT ⇒ 12.6825
Chapter 06
6. Bond Price & YTM on a Coupon Date
Pricing with TVM, semiannual coupons, yield to maturity, current market examples.
6.1 Method
P = Σt=1..N (C/m) / (1 + y/m)t + F / (1 + y/m)N
TVM mapping: N = years×m, I/Y = y/m, PMT = coupon/m, FV = face, solve PV
TVM mapping: N = years×m, I/Y = y/m, PMT = coupon/m, FV = face, solve PV
For YTM, enter the price as a negative PV, solve I/Y, then multiply by m (bond-equivalent yield). Indian G-secs and US Treasuries pay semiannually (m = 2); many corporate bonds pay annually.
Worked example — Bond prices
10-yr, 10% annual coupon, face 1,000, yield 8% (Schweser Book 4)
BA: 10 N 8 I/Y 100 PMT 1000 FV CPT PV ⇒ −1,134.2016
HP: 10 n 8 i 100 PMT 1000 FV PV
HP: 10 n 8 i 100 PMT 1000 FV PV
Same bond, semiannual (4% per half-year)
20 N 4 I/Y 50 PMT 1000 FV CPT PV ⇒ −1,135.9033
G-sec style: 10-yr 7.26% semiannual, face 100, yield 7.00%
BA: 20 N 3.5 I/Y 3.63 PMT 100 FV CPT PV ⇒ −101.8476
HP: 20 n 3.5 i 3.63 PMT 100 FV PV
HP: 20 n 3.5 i 3.63 PMT 100 FV PV
Worked example — Yield to maturity
100 a year for 10 years, price 700 (VRM Ch. 11)
BA: 10 N 700 +/− PV 100 PMT 0 FV CPT I/Y ⇒ 7.0728
HP: 10 n 700 CHS PV 100 PMT 0 FV i
HP: 10 n 700 CHS PV 100 PMT 0 FV i
Paid semiannually for 5 years
Same keys (N = 10) ⇒ periodic 7.0728; YTM = 7.0728 × 2 = 14.15% (Schweser rounds to 14.14%)
10-yr 6% semiannual bond, price 98.50
BA: 20 N 98.5 +/− PV 3 PMT 100 FV CPT I/Y ⇒ 3.1018 × 2 = 6.2035
HP: … i then 2 ×
Chapter 07
7. Between Coupons, Accrued Interest & Duration
Day counts, BA BOND worksheet, HP PRICE/YTM, clean vs. dirty, effective duration, convexity, DV01.
7.1 Day counts and accrued interest (VRM Ch. 9)
AI = (Coupon / m) × (days since last coupon / days in coupon period)
Dirty (full) price = Clean (quoted) price + AI
Dirty (full) price = Clean (quoted) price + AI
BA DATE worksheet:
2nd DATE DT1= date ENTER ↓ DT2= date ENTER ↓ DBD= CPT.
Dates as MM.DDYY (15 Nov 2029 = 11.1529). ↓ then 2nd SET toggles ACT/360.
HP: g M.DY; date1 ENTER date2 g ΔDYS ⇒ actual days; x≷y ⇒ 30/360 days. Dates as MM.DDYYYY (11.152029).
HP: g M.DY; date1 ENTER date2 g ΔDYS ⇒ actual days; x≷y ⇒ 30/360 days. Dates as MM.DDYYYY (11.152029).
7.2 BA II Plus BOND worksheet and HP PRICE / YTM
BA: 2nd BOND 2nd CLR WORK, then step with ↓:
SDT= settlement date ENTER → CPN= annual coupon % ENTER → RDT= maturity date ENTER → RV= 100 ENTER
→ ACT (2nd SET for 360) → 2/Y (2nd SET for 1/Y) → YLD= yield ENTER
→ PRI= CPT (clean price) → AI= (shown automatically).
To find yield: key the clean price at PRI= ENTER, move ↑ to YLD= CPT.
The BA II Plus Professional also shows DUR= (modified duration) after AI.
HP: yield i coupon % PMT settlement ENTER maturity f PRICE (gold, above yx) ⇒ clean price; x≷y ⇒ AI; + ⇒ dirty price. For yield: clean price PV coupon PMT settlement ENTER maturity f YTM (above 1/x). HP PRICE/YTM assume semiannual coupons, actual/actual days and redemption at 100. For annual-coupon or 30/360 bonds use the BA worksheet or the formula.
HP: yield i coupon % PMT settlement ENTER maturity f PRICE (gold, above yx) ⇒ clean price; x≷y ⇒ AI; + ⇒ dirty price. For yield: clean price PV coupon PMT settlement ENTER maturity f YTM (above 1/x). HP PRICE/YTM assume semiannual coupons, actual/actual days and redemption at 100. For annual-coupon or 30/360 bonds use the BA worksheet or the formula.
Worked example — 6% semiannual bond between coupon dates
Coupons 15 May / 15 Nov; matures 15 Nov 2034; settles 10 Mar 2030; yield 7%. Last coupon 15 Nov 2029, next 15 May 2030.
Days
BA: 2nd DATE 11.1529 ENTER ↓ 3.1030 ENTER ↓ CPT ⇒ DBD= 115;
period 11.1529 → 5.1530 ⇒ 181.
HP: 11.152029 ENTER 3.102030 g ΔDYS ⇒ 115
Accrued interest3 × 115/181 = 1.9061
Clean price
BA: 2nd BOND 3.1030 ENTER ↓ 6 ENTER ↓ 11.1534 ENTER ↓ 100 ENTER ↓ ↓ ↓ 7 ENTER ↓ CPT
⇒ PRI= 96.0535; ↓ ⇒ AI= 1.9061
HP: 7 i 6 PMT 3.102030 ENTER 11.152034 f PRICE ⇒ 96.0535; x≷y ⇒ 1.9061; + ⇒ 97.9596
HP: 7 i 6 PMT 3.102030 ENTER 11.152034 f PRICE ⇒ 96.0535; x≷y ⇒ 1.9061; + ⇒ 97.9596
Dirty price96.0535 + 1.9061 = 97.9596
Yield if clean = 97.00
BA: at PRI= key 97 ENTER, ↑ to YLD= CPT ⇒ 6.7551.
HP: 97 PV 6 PMT 3.102030 ENTER 11.152034 f YTM ⇒ 6.7551
7.3 Effective duration, convexity and DV01 by repricing (VRM Ch. 12)
D = (P− − P+) / (2 P0 Δy) |
C = (P+ + P− − 2P0) / [P0 (Δy)²] |
DV01 ≈ (P−1bp − P+1bp) / 2
Price the bond three times with TVM, changing only I/Y: at the yield, yield +Δy, yield −Δy. Store each price (STO 1, 2, 3) and apply the formulas. This works on any permitted calculator and matches how GARP defines effective duration.
Worked example — 10-yr 6% semiannual bond at 7%, Δy = 50 bp
Base price
20 N 3.5 I/Y 3 PMT 100 FV CPT PV
⇒ −92.8938 +/− STO 1 (HP: … PV CHS STO 1)
Yield +50 bp3.75 I/Y CPT PV ⇒ −89.5778 +/− STO 2
Yield −50 bp3.25 I/Y CPT PV ⇒ −96.3652 +/− STO 3
Duration(RCL 3 − RCL 2) ÷ (2 × RCL 1 × 0.005) = ⇒ 7.3065
Convexity(RCL 2 + RCL 3 − 2 × RCL 1) ÷ (RCL 1 × 0.005 x²) = ⇒ 66.92
DV01 (per 100 face)reprice at 3.495 and 3.505 (i.e. ±1 bp): (P− − P+)/2 = 0.0678
Chapter 08
8. NPV & IRR (Cash-Flow Worksheet)
Cash-flow worksheet, grouped (repeated) cash flows, both calculators.
8.1 Keys
BA: CF 2nd CLR WORK; CF0= amount ENTER ↓ C01= amount ENTER ↓ F01= how many times in a row ENTER ↓ …
then NPV I= rate ENTER ↓ CPT; IRR CPT.
HP: f REG; amount g CF0 (on PV); amount g CFj (on PMT); count g Nj (on FV) for repeats; rate i; f NPV (above PV); f IRR (above FV).
HP: f REG; amount g CF0 (on PV); amount g CFj (on PMT); count g Nj (on FV) for repeats; rate i; f NPV (above PV); f IRR (above FV).
NPV = Σt=0..N CFt / (1+r)t |
IRR: Σt=0..N CFt / (1+IRR)t = 0
Worked example — Project: −INR 10 lakh; then 3, 4, 4, 2 lakh; cost of capital 10%
BA
CF 2nd CLR WORK 1000000 +/− ENTER ↓ 300000 ENTER ↓ ↓
400000 ENTER ↓ 2 ENTER ↓ 200000 ENTER ↓
NPV 10 ENTER ↓ CPT ⇒ NPV= 40,434.3966;
IRR CPT ⇒ 11.9285
HP
f REG 1000000 CHS g CF0 300000 g CFj
400000 g CFj 2 g Nj 200000 g CFj
10 i f NPV ⇒ 40,434.3966;
f IRR ⇒ 11.9285
CheckNPV > 0 and IRR (11.93%) > 10% ⇒ accept. Consistent: NPV at the IRR is zero.
EXAM TRAP: BA: after keying a cash flow you must press ENTER before ↓, or it is not saved. The F-values default to 1 — press ↓ to skip them.
EXAM TRAP: HP: f REG is essential — old cash flows stay in memory. HP IRR may take a few seconds (“running”).
EXAM TRAP: The HP accepts up to 20 grouped cash flows with Nj up to 99; the BA up to 24 flows with frequency up to 9,999.
Chapter 09
9. Loan & Mortgage Amortisation
Level payment, interest vs. principal split, balance outstanding (FMP mortgages).
9.1 Keys
First solve the payment with TVM. Then:
BA: 2nd AMORT P1= first payment ENTER ↓ P2= last payment ENTER ↓
BAL= ↓ PRN= ↓ INT= (principal and interest paid over payments P1 to P2).
HP: after the payment is computed: 0 n; number of payments f AMORT (above n) ⇒ interest; x≷y ⇒ principal; RCL PV ⇒ remaining balance. Repeat for the next block (it continues from where it stopped). HP AMORT rounds each result to the number of decimals displayed — set f 2 for money.
HP: after the payment is computed: 0 n; number of payments f AMORT (above n) ⇒ interest; x≷y ⇒ principal; RCL PV ⇒ remaining balance. Repeat for the next block (it continues from where it stopped). HP AMORT rounds each result to the number of decimals displayed — set f 2 for money.
Payment = P0 × [i(1+i)n] / [(1+i)n − 1]
Worked example — 30-year USD 750,000 mortgage at 5% (monthly)
Payment
BA: 360 N 5 ÷ 12 = I/Y 750000 PV 0 FV CPT PMT
⇒ −4,026.1622.
HP: f 2 30 g 12× 5 g 12÷ 750000 PV 0 FV PMT
⇒ −4,026.16
Month 1
BA: 2nd AMORT 1 ENTER ↓ 1 ENTER ↓
⇒ BAL= 749,098.8378, PRN= −901.1622, INT= −3,125.0000.
HP: 0 n 1 f AMORT ⇒ −3,125.00; x≷y ⇒ −901.16; RCL PV ⇒ 749,098.84
Year 1 (1–12)
BA: P1 = 1, P2 = 12 ⇒ BAL= 738,934.7599, PRN= −11,065.2401, INT= −37,248.7060.
HP (recompute the payment first, then): 0 n 12 f AMORT, x≷y, RCL PV
(last-cent differences possible because of rounding)
Check12 × 4,026.16 = 48,313.95 ≈ 37,248.71 + 11,065.24 ✓ (Same as FMP formula sheet: interest 3,125, principal 901.16.)
Chapter 10
10. Statistics: One Variable
Mean, sample and population standard deviation (Quant Analysis).
10.1 Keys
BA: 2nd DATA 2nd CLR WORK; X01= value ENTER ↓ Y01= 1 (frequency; leave as 1) ↓ X02= …
then 2nd STAT, press 2nd SET until 1-V, then ↓: n, x̄, Sx (sample s.d.), σx (population s.d.), Σx, Σx².
HP: f Σ; each value Σ+; g x̄ (on 0) = mean; g s (on .) = sample s.d. (the HP has no population s.d. key — see trick below).
HP: f Σ; each value Σ+; g x̄ (on 0) = mean; g s (on .) = sample s.d. (the HP has no population s.d. key — see trick below).
x̄ = (Σ xi) / n |
s = √[Σ(xi − x̄)² / (n − 1)] (sample) |
σ = √[Σ(xi − x̄)² / n] (population)
Worked example — Monthly returns 2%, −1%, 3%, 4%, −2%
BA
2nd DATA 2nd CLR WORK 2 ENTER ↓ ↓
1 +/− ENTER ↓ ↓ 3 ENTER ↓ ↓
4 ENTER ↓ ↓ 2 +/− ENTER;
2nd STAT (1-V) ↓ ⇒ n= 5, x̄= 1.2000, Sx= 2.5884, σx= 2.3152
HP
f Σ 2 Σ+ 1 CHS Σ+ 3 Σ+ 4 Σ+ 2 CHS Σ+
(display 5.0000); g x̄ ⇒ 1.2000; g s ⇒ 2.5884
HP population s.d. trick
After the above: g x̄ Σ+ g s ⇒ 2.3152
(adding the mean as an extra point turns n − 1 into n). Then g x̄ g Σ− to remove it again.
Chapter 11
11. Statistics: Regression, Correlation, Beta
Two-variable data, slope, intercept, correlation, covariance, forecasts (Quant Analysis).
11.1 Keys
BA: 2nd DATA 2nd CLR WORK; X01= x ENTER ↓ Y01= y ENTER ↓ …;
2nd STAT, 2nd SET until LIN; ↓: n, x̄, Sx, σx, ȳ, Sy, σy, a (intercept), b (slope), r (correlation), X′, Y′
(key a value, CPT the other to forecast).
HP: f Σ; for each pair: y ENTER x Σ+ (y first!). g x̄ ⇒ x̄, x≷y ⇒ ȳ; g s ⇒ sx, x≷y ⇒ sy; value of x g ŷ,r (on 2) ⇒ ŷ, x≷y ⇒ r.
HP: f Σ; for each pair: y ENTER x Σ+ (y first!). g x̄ ⇒ x̄, x≷y ⇒ ȳ; g s ⇒ sx, x≷y ⇒ sy; value of x g ŷ,r (on 2) ⇒ ŷ, x≷y ⇒ r.
b = r (sy/sx) = Cov(x,y) / sx² |
a = ȳ − b x̄ |
Covsample = r sx sy |
βstock = b when x = market
Worked example — Beta of a stock against NIFTY 50 (six monthly returns, %)
NIFTY (x): 1.2, −0.8, 2.1, 0.5, −1.5, 1.9 Stock (y): 1.8, −1.5, 2.6, 0.2, −2.4, 2.5
BA
2nd DATA 2nd CLR WORK 1.2 ENTER ↓ 1.8 ENTER ↓
0.8 +/− ENTER ↓ 1.5 +/− ENTER ↓ … (all six pairs);
2nd STAT (LIN) ↓ ⇒ n= 6, x̄= 0.5667, Sx= 1.4610,
ȳ= 0.5333, Sy= 2.1257, a= −0.2873, b= 1.4482, r= 0.9953
HP
f Σ 1.8 ENTER 1.2 Σ+ 1.5 CHS ENTER 0.8 CHS Σ+ …;
0 g ŷ,r ⇒ −0.2873 (= a), x≷y ⇒ 0.9953 (= r);
1 g ŷ,r ⇒ 1.1609; slope b = 1.1609 − (−0.2873) = 1.4482
Results
Beta = 1.448; correlation 0.995; R² = 0.9953² = 0.991;
sample covariance = 0.9953 × 1.4610 × 2.1257 = 3.0913;
forecast at NIFTY = 1%: ŷ = 1.161%.
Chapter 12
12. Probability-Weighted Mean & Standard Deviation
Expected return and risk from scenarios (Quant Analysis; FMP).
12.1 Formulas and the BA frequency trick
E(R) = Σ pi Ri |
σ² = Σ pi [Ri − E(R)]²
BA: enter each return as X and its probability ×100 as the frequency Y (whole numbers only).
Then 2nd STAT (1-V): x̄ = E(R) and σx (population) = probability-weighted s.d.
HP: weighted mean with R ENTER p Σ+ for each scenario, then g x̄w (on 6). The HP has no weighted s.d. key — compute σ² by the formula with STO / RCL.
HP: weighted mean with R ENTER p Σ+ for each scenario, then g x̄w (on 6). The HP has no weighted s.d. key — compute σ² by the formula with STO / RCL.
Worked example — Three scenarios: 15% (p = 0.30), 5% (0.50), −10% (0.20)
BA
2nd DATA 2nd CLR WORK 15 ENTER ↓ 30 ENTER ↓
5 ENTER ↓ 50 ENTER ↓ 10 +/− ENTER ↓ 20 ENTER;
2nd STAT (1-V) ⇒ n= 100, x̄= 5.0000, σx= 8.6603
HP
f Σ 15 ENTER 0.3 Σ+ 5 ENTER 0.5 Σ+
10 CHS ENTER 0.2 Σ+ g x̄w ⇒ 5.0000.
Variance: 0.3 ENTER 10 g x² × 0.5 ENTER 0 × +
0.2 ENTER 15 g x² × + g √x ⇒ 8.6603
CheckE(R) = 4.5 + 2.5 − 2.0 = 5.0%; σ² = 0.3(10²) + 0.5(0²) + 0.2(15²) = 75 ⇒ σ = 8.66% ✓
EXAM TRAP: In the BA probability trick, read σx, not Sx — the scenario probabilities describe the whole population.
EXAM TRAP: For sample data (historical returns) use Sx (BA) or g s (HP). FRM questions on “volatility estimated from a sample” want the sample s.d.
Chapter 13
13. Memory, Speed Tricks & Common Errors
Store and recall, chain calculations, error messages, exam-day checklist.
13.1 Memory
BA: value STO n and RCL n for n = 0–9. Memory arithmetic: STO + 1 adds the display to M1.
2nd MEM 2nd CLR WORK clears all memories.
HP: value STO n and RCL n for n = 0–9 and .0–.9 (fewer on some models when programs are stored). STO + 1 adds to R1. Do not use R1–R6 while doing statistics — the HP keeps its Σ sums there. Store intermediate results instead of re-typing rounded values — e.g. store u and d in a binomial tree, or P0, P+, P− for duration. It removes rounding errors and saves time.
HP: value STO n and RCL n for n = 0–9 and .0–.9 (fewer on some models when programs are stored). STO + 1 adds to R1. Do not use R1–R6 while doing statistics — the HP keeps its Σ sums there. Store intermediate results instead of re-typing rounded values — e.g. store u and d in a binomial tree, or P0, P+, P− for duration. It removes rounding errors and saves time.
Common errors and how to fix them
| Symptom | Fix |
|---|---|
| Answer is off by a large factor | BA P/Y is 12 (or C/Y ≠ P/Y). Set 2nd P/Y 1 ENTER. |
| Error 5 (TVM, IRR) | Signs: PV and FV/PMT must have opposite signs; IRR needs at least one sign change. |
| TVM answer slightly wrong | BGN mode left on; old PMT/FV not cleared; decimals too few (use 4). |
| BA arithmetic “wrong” | Method is Chn, not AOS. Set AOS or use brackets. |
| BA worksheet value not saved | Pressed ↓ without ENTER. |
| Dates rejected | BA uses MM.DDYY (years 1950–2049); HP uses MM.DDYYYY after g M.DY. Using the wrong format swaps day and month. |
| HP gives nonsense | Stack confusion: press ENTER between two typed numbers; clear with f REG. |
| Percent vs. decimal | TVM keys take 8 for 8%; formulas (e.g. erT) need 0.08. |
| Negative number typed wrongly | Use +/− (BA) or CHS (HP) after the digits, not the minus key. |
Exam-day checklist
| When | Action |
|---|---|
| Before the exam | Model is on GARP’s list; fresh battery (spare); practised every chapter of this guide on your calculator. |
| At the start | BA: P/Y = 1, 4 decimals, AOS, END mode. HP: f 4, END, M.DY. |
| Every question | Clear TVM/worksheet (BA) or f FIN / f REG (HP). Write the TVM inputs on the scratch sheet before keying. |
| Sanity checks | Premium bond if coupon > yield; annuity due = ordinary ×(1 + i); IRR > hurdle ⇔ NPV > 0; population s.d. < sample s.d. |
Chapter 14
14. One-Page Quick-Reference Card
Print and keep in your formula notebook.
| Task | BA II Plus | HP 12C |
|---|---|---|
| Setup | 2nd P/Y 1 ENTER; 2nd FORMAT 4 ENTER; AOS; END | f 4; g END; g M.DY |
| Clear | 2nd CLR TVM; 2nd CLR WORK | f FIN; f REG; f Σ |
| TVM | N, I/Y, PV, PMT, FV; CPT key | n, i, PV, PMT, FV; press key |
| Monthly | N = 12×yrs, I/Y = rate/12 | g 12×, g 12÷ |
| Annuity due | 2nd BGN 2nd SET | g BEG |
| ex / ln | 2nd ex / LN | g ex / g LN |
| yx | y yx x = | y ENTER x yx |
| n!, nCr | 2nd x!, 2nd nCr | g n!; nCr via factorials |
| Rate conversion | 2nd ICONV: NOM, EFF, C/Y | formula or TVM trick |
| Days between dates | 2nd DATE: DT1, DT2, DBD | g ΔDYS |
| Bond price / AI | 2nd BOND: SDT, CPN, RDT, RV, ACT, 2/Y, YLD, PRI, AI | f PRICE; x≷y = AI |
| Bond yield | BOND: key PRI, CPT YLD | price PV … f YTM |
| NPV / IRR | CF CF0, C01, F01…; NPV, IRR | g CF0, g CFj, g Nj; f NPV, f IRR |
| Amortisation | 2nd AMORT: P1, P2, BAL, PRN, INT | 0 n; k f AMORT; x≷y; RCL PV |
| 1-var stats | 2nd DATA; 2nd STAT 1-V: x̄, Sx, σx | Σ+; g x̄, g s |
| Regression | 2nd STAT LIN: a, b, r | y ENTER x Σ+; g ŷ,r |
| Weighted mean | Y = probability ×100; read x̄, σx | R ENTER p Σ+; g x̄w |
| Memory | STO / RCL 0–9 | STO / RCL 0–9, .0–.9 |
Prepared by RBei Classes for FRM Part I revision. Keystroke sequences follow the Texas Instruments BA II Plus and HP 12C owner’s manuals; display formats can differ slightly between model editions, so practise on your own calculator. GARP® and FRM® are trademarks of the Global Association of Risk Professionals, which does not endorse this material. BA II Plus is a trademark of Texas Instruments; HP 12C of HP Inc. Always confirm the permitted-calculator list on garp.org.
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FAQ
FRM Calculator Guide FAQs
GARP permits the Texas Instruments BA II Plus (including Professional) and Hewlett Packard models including the HP 12C family, HP 10B II, HP 10BII+ and HP 20B. Any other calculator means the exam is not graded. Always re-check the current list on garp.org before your exam.
BA II Plus uses algebraic entry and is common in Indian coaching material, with bond, date and amortisation worksheets. HP 12C uses RPN, is very fast once learnt, and has built-in PRICE/YTM and date functions. This guide covers both.
On the BA II Plus, a reset leaves P/Y = 12, so keying 8 in I/Y means 8%/12 per period and every TVM answer is wrong. Set P/Y = 1, use END mode, clear TVM before each question, and watch sign convention (outflows negative).
Yes. The RBei Classes FRM Part 1 Calculator Guide (BA II Plus & HP 12C) PDF is free to download — no payment required. Use the Download PDF buttons on this page for an instant copy.
Fourteen chapters: permitted calculators and setup, HP 12C RPN, maths keys and FRM formulas, TVM, interest-rate conversion, bond price and YTM, accrued interest and duration, NPV/IRR, amortisation, one-variable statistics, regression and beta, probability-weighted risk, memory and common errors, plus a one-page quick-reference card.
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