Free SOA Exam FM (Financial Mathematics) Formula Sheet (2026)

Every Exam FM formula you need on the test, grouped by topic and rendered with full math notation. 96 formulas across 5 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

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All Exam FM Formulas

Time Value of Money 19 items
Accumulation factor — compound interest
a(t)=(1+i)ta(t)=(1+i)^t
ii = annual effective interest rate, tt = time in years
Present value factor
v=11+i=1−dv=\dfrac{1}{1+i}=1-d
dd = annual effective discount rate
Relationship: \(d\), \(i\), \(v\)
d=i1+i=1−v,v=11+id=\dfrac{i}{1+i}=1-v,\quad v=\dfrac{1}{1+i}
Nominal rate \(i^{(m)}\) vs effective rate
(1+i(m)m)m=1+i\left(1+\dfrac{i^{(m)}}{m}\right)^m = 1+i
mm = compounding periods per year
Force of interest
δ=ln⁡(1+i)\delta = \ln(1+i)
eδ=1+i,a(t)=eδte^{\delta} = 1+i,\quad a(t)=e^{\delta t}
Simple interest accumulation
a(t)=1+ita(t)=1+it
Used for short periods (< 1 year) and treasury bills
Accumulation function a(t) from time 0 under a variable force of interest
a(t)=e∫0tδ(s) dsa(t) = e^{\int_0^t \delta(s)\,ds}, a(t) = accumulated value of 1, δ(s)\delta(s) = force of interest at time s
Effective rate of interest in the nth period
in=a(n)−a(n−1)a(n−1)i_n = \dfrac{a(n) - a(n-1)}{a(n-1)}, a(t) = accumulation function, n = period index
Real rate of interest
i′=i−r1+ri' = \dfrac{i - r}{1 + r}, i' = real rate, i = nominal (effective) interest rate, r = inflation rate
Future value of a single sum
FV=P(1+i)nFV = P(1 + i)^n, P = principal invested at time 0, i = effective rate per period, n = number of periods
Solving for the unknown number of periods
n=ln⁡(FV/PV)ln⁡(1+i)n = \frac{\ln(FV/PV)}{\ln(1+i)}, n = number of periods, FV = future value, PV = present value, i = effective rate per period
General accumulation factor between times \(t_1\) and \(t_2\) under a variable force of interest
a(t1,t2)=e∫t1t2δ(s) dsa(t_1, t_2) = e^{\int_{t_1}^{t_2} \delta(s)\,ds}, δ(s)\delta(s) = force of interest at time s, t1t_1 = start time, t2t_2 = end time
Compound interest doubling time
n=ln⁡2ln⁡(1+i)n = \frac{\ln 2}{\ln(1+i)}, n = years to double, i = annual effective rate
Solving for the unknown effective interest rate
i=(FVPV)1/n−1i = \left(\frac{FV}{PV}\right)^{1/n} - 1, FV = future value, PV = present value, n = number of periods, i = annual effective rate
Nominal discount rate to effective annual rate
1+i=(1−d(m)m)−m1 + i = \left(1 - \frac{d^{(m)}}{m}\right)^{-m}, i = effective annual interest rate, d^{(m)} = nominal discount rate convertible m-thly, m = compounding frequency
Nominal discount rate from present value factor
d(m)=m(1−v1/m)d^{(m)} = m\left(1 - v^{1/m}\right), d^{(m)} = nominal discount rate convertible m-thly, v = present value factor = 1/(1+i), m = compounding frequency
Ordering of interest and discount rates
d<d(m)<δ<i(m)<id < d^{(m)} < \delta < i^{(m)} < i, d = effective discount, d^{(m)} = nominal discount, δ = force of interest, i^{(m)} = nominal interest, i = effective interest, m ≥ 1
Force of interest from nominal interest rate
δ=mln⁡(1+i(m)m)\delta = m\ln\left(1 + \frac{i^{(m)}}{m}\right), δ = force of interest, i^{(m)} = nominal interest rate convertible m-thly, m = compounding frequency
Linear interpolation estimate of the yield rate
i∗≈iL+(iH−iL)⋅NPVLNPVL−NPVH i^* \approx i_L + (i_H - i_L) \cdot \frac{NPV_L}{NPV_L - NPV_H} , i* = yield rate, iLi_L/iHi_H = low/high test rates, NPVLNPV_L/NPVHNPV_H = NPV at each rate
Annuities and Non-Contingent Cash Flows 23 items
Annuity-immediate (end of period) PV
an‾∣=1−vnia_{\overline{n}|}=\dfrac{1-v^n}{i}
nn payments of 1 at end of each period; v=(1+i)−1v=(1+i)^{-1}
Annuity-due (beginning of period) PV
a¨n‾∣=1−vnd=(1+i) an‾∣\ddot{a}_{\overline{n}|}=\dfrac{1-v^n}{d}=(1+i)\,a_{\overline{n}|}
Annuity-immediate — accumulated value
sn‾∣=(1+i)n−1i=(1+i)n an‾∣s_{\overline{n}|}=\dfrac{(1+i)^n-1}{i}=(1+i)^n\,a_{\overline{n}|}
Deferred annuity PV
k∣an‾∣=vk an‾∣_{k|}a_{\overline{n}|}=v^k\,a_{\overline{n}|}
(annuity starting kk periods from now)
Increasing annuity-immediate PV
(Ia)n‾∣=a¨n‾∣−nvni(I a)_{\overline{n}|}=\dfrac{\ddot{a}_{\overline{n}|}-n v^n}{i}
Payments: 1,2,…,n1,2,\ldots,n
Decreasing annuity-immediate PV
(Da)n‾∣=n−an‾∣i(D a)_{\overline{n}|}=\dfrac{n - a_{\overline{n}|}}{i}
Payments: n,n−1,…,1n,n-1,\ldots,1
Continuously paid annuity PV
aˉn‾∣=1−e−δnδ\bar{a}_{\overline{n}|}=\dfrac{1-e^{-\delta n}}{\delta}
Mthly annuity-immediate PV
an‾∣(m)=1−vni(m)a_{\overline{n}|}^{(m)}=\dfrac{1-v^n}{i^{(m)}}
mnmn payments of 1/m1/m per period
Geometric annuity present value
PV=1−(1+g1+i)ni−gPV = \frac{1 - \left(\frac{1+g}{1+i}\right)^n}{i - g} (i ≠ g), g = payment growth rate, i = effective rate, n = number of payments
Increasing arithmetic perpetuity present value
(Ia)∞∣‾=1id,(Ia¨)∞∣‾=1d2(Ia)_{\overline{\infty\vert}} = \frac{1}{id}, \quad (I\ddot{a})_{\overline{\infty\vert}} = \frac{1}{d^2}, i = effective interest rate, d = effective discount rate
Annuity-due to annuity-immediate relationship
a¨n∣‾=(1+i) an∣‾\ddot{a}_{\overline{n\vert}} = (1+i)\, a_{\overline{n\vert}}, i = effective interest rate, n = number of payments
Perpetuity present value (immediate and due)
a∞∣‾=1i,a¨∞∣‾=1da_{\overline{\infty\vert}} = \frac{1}{i}, \quad \ddot{a}_{\overline{\infty\vert}} = \frac{1}{d}, i = effective interest rate, d = effective discount rate
Solving for the term of a level annuity
n=−ln⁡(1−i⋅PVP)ln⁡(1+i)n = -\dfrac{\ln\left(1 - \frac{i \cdot PV}{P}\right)}{\ln(1+i)}, n = number of payments, i = periodic rate, PV = present value, P = payment; requires P>i⋅PVP > i \cdot PV
Arithmetic increasing annuity present value
PV=(P−Q) an∣‾+Q (Ia)n∣‾PV = (P - Q)\,a_{\overline{n\vert}} + Q\,(Ia)_{\overline{n\vert}}, P = first payment, Q = annual increase, n = number of payments, a,(Ia)a,(Ia) = level and increasing annuity factors
Annuity payment from present value
P=PVan∣‾P = \dfrac{PV}{a_{\overline{n\vert}}}, P = level payment, PV = present value, an∣‾a_{\overline{n\vert}} = annuity-immediate factor (use a¨n∣‾\ddot{a}_{\overline{n\vert}} for due)
Geometric growing perpetuity present value
PV=Pi−gPV = \frac{P}{i - g} (valid only when g < i), P = first payment, g = growth rate per period, i = effective interest rate
Decreasing annuity-immediate accumulated value
(Ds)n∣‾=n(1+i)n−sn∣‾i(Ds)_{\overline{n\vert}} = \frac{n(1+i)^n - s_{\overline{n\vert}}}{i}, n = number of payments, i = effective rate, s = annuity-immediate accumulated value factor
Modified rate for valuing a geometric annuity as level
j=i−g1+gj = \frac{i - g}{1 + g}, j = equivalent level rate, i = effective interest rate, g = geometric growth rate per period
Increasing annuity-immediate accumulated value
(Is)n∣‾=s¨n∣‾−ni(Is)_{\overline{n\vert}} = \frac{\ddot{s}_{\overline{n\vert}} - n}{i}, n = number of payments, i = effective rate, ä = annuity-due accumulated value factor
Accumulated value of an annuity payable m-thly
sn∣‾(m)=(1+i)n−1i(m)=ii(m) sn∣‾s_{\overline{n\vert}}^{(m)} = \frac{(1+i)^n - 1}{i^{(m)}} = \frac{i}{i^{(m)}}\,s_{\overline{n\vert}}, i = annual effective rate, i^{(m)} = nominal rate compounded m-thly, n = years
Present value of a continuously varying payment stream
PV=∫0nf(t) exp⁡ ⁣(−∫0tδ(s) ds)dtPV = \int_0^n f(t)\,\exp\!\left(-\int_0^t \delta(s)\,ds\right)dt, f(t) = payment rate at time t, δ(s) = force of interest, n = term
Continuously increasing annuity present value
(Iˉaˉ)n∣‾=aˉn∣‾−nvnδ(\bar{I}\bar{a})_{\overline{n\vert}} = \frac{\bar{a}_{\overline{n\vert}} - nv^n}{\delta}, aˉn∣‾\bar{a}_{\overline{n\vert}} = level continuous annuity PV, v = present value factor, n = term, δ = force of interest
Continuous perpetuity present value
aˉ∞∣‾=1δ\bar{a}_{\overline{\infty\vert}} = \frac{1}{\delta}, δ = force of interest =ln⁡(1+i)= \ln(1+i)
Loans 15 items
Prospective loan balance
Bt=P an−t‾∣B_t = P\,a_{\overline{n-t}|}
PV of remaining n−tn-t payments; PP=level payment
Retrospective loan balance
Bt=L(1+i)t−P st‾∣B_t = L(1+i)^t - P\,s_{\overline{t}|}
LL=original loan, PP=level payment
Interest and principal portions of payment \(k\)
Interest: Ik=i Bk−1I_k = i\,B_{k-1}
Principal: PRk=P−IkPR_k = P - I_k
Sinking fund method — annual cost
Annual cost =iL+Lsn‾∣j= iL + \dfrac{L}{s_{\overline{n}|j}}
ii=loan rate, jj=sinking fund rate, LL=loan
Principal repaid over a block of payments
∑t=j+1kPt=Bj−Bk\sum_{t=j+1}^k P_t = B_j - B_k, PtP_t = principal in payment t, BjB_j = balance after payment j, BkB_k = balance after payment k
Final drop or balloon payment
Rfinal=Bn−1(1+i)R_{\text{final}} = B_{n-1}(1+i), RfinalR_{\text{final}} = exact last payment, Bn−1B_{n-1} = balance after the last full payment, i = periodic rate; drop if < R, balloon if > R
Total interest paid over the life of a loan
∑t=1nIt=nR−L\sum_{t=1}^n I_t = nR - L, ItI_t = interest in payment t, n = number of payments, R = level payment, L = loan principal
Amortized loan level payment
R=Lan∣i‾R = \dfrac{L}{a_{\overline{n\vert i}}}, R = level end-of-period payment, L = loan principal, an∣i‾a_{\overline{n\vert i}} = annuity-immediate factor, n = number of payments, i = periodic rate
Recursive loan balance update
Bt=Bt−1(1+it)−RtB_t = B_{t-1}(1+i_t) - R_t, BtB_t = balance after payment t, iti_t = rate charged in period t, RtR_t = payment made at time t
Total interest over a block of payments
∑t=j+1kIt=(k−j)R−(Bj−Bk)\sum_{t=j+1}^{k} I_t = (k-j)R - (B_j - B_k), R = level payment, BjB_j = balance after payment j, BkB_k = balance after payment k
Refinanced loan new payment
R′=Btan′∣i′‾R' = \dfrac{B_t}{a_{\overline{n'\vert i'}}}, BtB_t = outstanding balance at refinance date, n' = new term in periods, i' = new periodic rate, R' = new level payment
Lender's realized yield with reinvestment
i=(R⋅sn∣j‾L)1/n−1i = \left(\dfrac{R \cdot s_{\overline{n\vert j}}}{L}\right)^{1/n} - 1, L = loan amount, R = payment, j = reinvestment rate, n = number of periods, i = realized annual yield
Interest-only period payment
RIO=iLR_{IO} = iL, i = periodic rate, L = loan principal (balance stays at L since no principal is repaid)
Total interest across a loan restructure
Total interest=tR+n′R′−L\text{Total interest} = tR + n'R' - L, t = phase-1 payments, R = original payment, n' = phase-2 payments, R' = new payment, L = original principal
Amortizing payment after an interest-only period
R=Lan−k∣i‾R = \dfrac{L}{a_{\overline{n-k\vert i}}}, L = principal, n = total term, k = interest-only periods, i = periodic rate, R = level payment
Bonds 18 items
Bond price formula
P=Fr an‾∣+CvnP = Fr\,a_{\overline{n}|} + Cv^n
FF=face, rr=coupon rate, CC=redemption, nn=periods, yield ii
Premium/discount bond formula
P−C=(Fr−Ci) an‾∣P - C = (Fr - Ci)\,a_{\overline{n}|}
Premium if Fr>CiFr>Ci; discount if Fr<CiFr<Ci
Makeham bond formula
P=K+gi(C−K)P = K + \dfrac{g}{i}(C-K)
K=CvnK=Cv^n, g=Fr/Cg=Fr/C (modified coupon rate)
Bond book value at time t
BVt=Fr⋅an−t∣i‾+C⋅vn−t=C+(Fr−Ci)⋅an−t∣i‾BV_t = Fr \cdot a_{\overline{n-t\vert i}} + C \cdot v^{n-t} = C + (Fr - Ci) \cdot a_{\overline{n-t\vert i}}, F = face value, r = coupon rate, C = redemption, i = original yield, n = total periods, t = elapsed periods
Discount accumulation write-up in period t
Write-upt=i⋅BVt−1−Fr=(Ci−Fr)⋅vn−t+1\text{Write-up}_t = i \cdot BV_{t-1} - Fr = (Ci - Fr) \cdot v^{n-t+1}, Fr = coupon, C = redemption, i = yield, BV = book value, n = total periods, t = period
Premium write-down in period t
Write-downt=Fr−i⋅BVt−1=(Fr−Ci)⋅vn−t+1\text{Write-down}_t = Fr - i \cdot BV_{t-1} = (Fr - Ci) \cdot v^{n-t+1}, Fr = coupon, C = redemption, i = yield, BV = book value, n = total periods, t = period
Accumulated value of a bond with coupon reinvestment
AV=Fr⋅sn∣j‾+CAV = Fr \cdot s_{\overline{n\vert j}} + C, Fr = coupon per period, j = reinvestment rate per period, n = number of coupons, C = redemption value
Solving a bond for its coupon rate
r=P−CvnF an∣i‾r = \dfrac{P - C v^n}{F\, a_{\overline{n\vert i}}}, P = price, C = redemption value, v = 1/(1+i), n = coupons, F = face, i = yield, r = per-period coupon rate
Solving a bond for its term
an∣i‾=P−CFr−Cia_{\overline{n\vert i}} = \dfrac{P-C}{Fr-Ci}, then vn=1−i an∣i‾v^n = 1 - i\,a_{\overline{n\vert i}}; P = price, C = redemption, Fr = coupon, Ci = yield income, i = yield, n = coupons
Total premium amortized through time t
P−BVt=(Fr−Ci)(an∣‾−an−t∣‾)P - BV_t = (Fr - Ci)(a_{\overline{n\vert}} - a_{\overline{n-t\vert}}), P = price, BVtBV_t = book value at t, Fr = coupon, Ci = yield income, n = coupons, t = periods elapsed
Bond salesman's yield approximation
i≈Fr+(C−P)/n(P+C)/2i \approx \dfrac{Fr + (C-P)/n}{(P+C)/2}, F = face, r = per-period coupon rate, C = redemption value, P = price, n = number of coupons, i = per-period yield
Call premium
Call premium=Ck−F \text{Call premium} = C_k - F , CkC_k = call price at date k, F = par value
Callable bond worst-case price
P=min⁡k[Fr⋅ak∣i‾+Ck⋅vk] P = \min_{k} \left[Fr \cdot a_{\overline{k\vert i}} + C_k \cdot v^k\right] , F = par, r = coupon rate, i = min yield, a = annuity factor, CkC_k = call price at date k, v = present value factor, k = call date
Call price premium-discount threshold
C∗=Fr/i C^* = Fr/i , C* = threshold call price, F = par, r = coupon rate, i = minimum yield per period; call prices below C* price at earliest call, above C* price at maturity
Bond book value adjustment in a coupon period
At=Fr−i⋅BVt−1=(Fr−Ci) vn−t+1A_t = Fr - i\cdot BV_{t-1} = (Fr - Ci)\,v^{n-t+1}, Fr = coupon, C = redemption value, i = yield, v = 1/(1+i), n = periods, t = period
Coupon minus yield interest from a known adjustment
Fr−Ci=Atvn−t+1Fr - Ci = \dfrac{A_t}{v^{n-t+1}}, AtA_t = adjustment in period t, Fr = coupon, Ci = yield interest on par, v = 1/(1+i), n = periods, t = period
Interest earned in a coupon period of a bond
It=i⋅BVt−1I_t = i \cdot BV_{t-1}, ItI_t = interest earned in period t, i = original purchase yield, BVt−1BV_{t-1} = book value at start of period
Sum of bond amortization adjustments
∑t=1nAt=∣P−C∣\sum_{t=1}^{n} A_t = |P - C|, AtA_t = period adjustment, P = purchase price, C = redemption value; the total premium or discount
General Cash Flows, Portfolios, and Asset-Liability Management 21 items
Macaulay duration
DMac=∑tt vt CFt∑tvt CFtD_{\text{Mac}} = \dfrac{\sum_t t\,v^t\,CF_t}{\sum_t v^t\,CF_t}
Weighted average time of cash flows
Modified duration
Dmod=DMac1+iD_{\text{mod}} = \dfrac{D_{\text{Mac}}}{1+i}
ΔP≈−Dmod P Δi\Delta P \approx -D_{\text{mod}}\,P\,\Delta i
Convexity
C=1Pd2Pdi2C = \dfrac{1}{P}\dfrac{d^2P}{di^2}
Price approximation: ΔP≈−Dmod P Δi+12C P (Δi)2\Delta P \approx -D_{\text{mod}}\,P\,\Delta i + \tfrac{1}{2}C\,P\,(\Delta i)^2
Immunization (Redington) conditions
1. PVassets=PVliabilitiesPV_{\text{assets}}=PV_{\text{liabilities}}
2. Dassets=DliabilitiesD_{\text{assets}}=D_{\text{liabilities}} (durations match)
3. Cassets>CliabilitiesC_{\text{assets}}>C_{\text{liabilities}} strictly (convexity)
First two zero surplus and its slope; strict convexity makes the current rate a local minimum.
Forward interest rate
(1+in)n(1+fn,m)m=(1+in+m)n+m(1+i_n)^n(1+f_{n,m})^m=(1+i_{n+m})^{n+m}
fn,mf_{n,m} = mm-year forward rate starting in nn years
Net present value
NPV=∑t=0nvt CFtNPV = \sum_{t=0}^{n} v^t\,CF_t
Accept project if NPV>0NPV>0
Second-order price approximation with convexity
ΔPP≈−Dmod Δi+12Cmod(Δi)2\frac{\Delta P}{P} \approx -D_{\text{mod}}\,\Delta i + \tfrac{1}{2}C_{\text{mod}}(\Delta i)^2, DmodD_{mod} = modified duration, CmodC_{mod} = modified convexity, Δi = change in yield rate
First-order price approximation using modified duration
ΔPP≈−Dmod⋅Δi\frac{\Delta P}{P} \approx -D_{\text{mod}} \cdot \Delta i, ΔP/P = relative price change, DmodD_{mod} = modified duration, Δi = change in yield rate (decimal)
Modified convexity from Macaulay measures
Cmod=Cmac+Dmac(1+i)2C_{\text{mod}} = \frac{C_{\text{mac}} + D_{\text{mac}}}{(1+i)^2}, CmodC_{mod} = modified convexity, CmacC_{mac} = Macaulay convexity, DmacD_{mac} = Macaulay duration, i = effective yield
Spot rate price of a zero-coupon bond
PV=1(1+st)tPV = \frac{1}{(1 + s_t)^t}, PV = present value of $1 at time t, sts_t = spot rate for maturity t, t = time to maturity in years
First-order Macaulay approximation (multiplicative)
P(i)≈P(i0)(1+i01+i)Dmac P(i) \approx P(i_0)\left(\frac{1+i_0}{1+i}\right)^{D_{\text{mac}}} , P = price, i = new yield, i₀ = base yield, DmacD_{mac} = Macaulay duration
Portfolio modified duration
Dmodport=∑jwjDmod,j D_{\text{mod}}^{\text{port}} = \sum_j w_j D_{\text{mod},j} , wjw_j = PVjPV_j/ΣPV = PV weight of asset j, DmodD_{mod},j = modified duration of asset j
Modified convexity
Cmod=∑tt(t+1)CFtvt+2P C_{\text{mod}} = \frac{\sum_t t(t+1) CF_t v^{t+2}}{P} , CFtCF_t = cash flow at t, v = 1/(1+i), P = price, i = yield
Present value under a non-flat yield curve
PV=∑tCFt(1+st)t PV = \sum_t \frac{CF_t}{(1+s_t)^t} , CFtCF_t = cash flow at time t, sts_t = spot rate for term t
Immunization asset amount shortcut for two zeros
P2=D−t1t2−t1⋅PVLP_2 = \dfrac{D - t_1}{t_2 - t_1} \cdot PV_L, P2P_2 = PV in longer zero, D = liability Macaulay duration, t1t_1,t2t_2 = zero maturities, PVLPV_L = liability present value
Duration-matching two-equation system for two zeros
P1+P2=PVL,  t1P1+t2P2=D⋅PVLP_1 + P_2 = PV_L,\; t_1 P_1 + t_2 P_2 = D \cdot PV_L, P1P_1,P2P_2 = PVs invested, t1t_1,t2t_2 = maturities, D = liability duration, PVLPV_L = liability PV
Modified convexity of a zero-coupon bond
Cmod=t(t+1)(1+i)2C_{\text{mod}} = \dfrac{t(t+1)}{(1+i)^2}, t = time to maturity, i = effective periodic yield
Macaulay convexity of a two-zero asset portfolio
Cmac(A)=t12P1+t22P2P1+P2C_{\text{mac}}(A) = \dfrac{t_1^2 P_1 + t_2^2 P_2}{P_1 + P_2}, t1t_1,t2t_2 = zero maturities, P1P_1,P2P_2 = PVs invested at each
One-year forward rate from adjacent spot rates
ft,t+1=(1+st+1)t+1(1+st)t−1f_{t,t+1} = \frac{(1+s_{t+1})^{t+1}}{(1+s_t)^t} - 1, f = forward rate from t to t+1, s = spot rate, t = time in years (larger accumulation factor on top)
Accumulation factor from a zero priced as a fraction of redemption
AF=1pAF = \frac{1}{p}, AF = accumulation factor (redemption per dollar invested), p = price as a fraction of redemption value (p is the discount factor)
Spot rate as geometric mean of one-year forwards
(1+sn)n=(1+f0,1)(1+f1,2)⋯(1+fn−1,n)(1+s_n)^n = (1+f_{0,1})(1+f_{1,2})\cdots(1+f_{n-1,n}), sns_n = n-year spot rate, f = one-year forward rate, f0,1f_{0,1} = s1s_1, n = number of years
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FreeFellow was built by Jeffrey Ting, a credentialed actuary and CFA charterholder who passed thirteen of the hardest exams in finance on the first attempt, and paid four-figure prep fees for every one. The learning itself was always free. The price was a moat.

So he started writing his own questions, then lessons, then mock exams, until it grew into a full prep platform covering 40 finance credentials with more than 45,000 original practice questions. The name says exactly what it is: the question bank is free, and Fellow is what you become once you pass.

01
Cost shouldn't decide who gets in.

The exam is a fair gate. A four-figure prep course is not. FreeFellow takes the second gate down, so the exam is the only one left.

02
Free should mean free.

No trial clock, no email gate, no credit card. The question bank, worked solutions, lessons, and readiness score stay free, and they are enough to pass.

03
Built by someone who sat where you sit.

He paid for the big-name courses, found nothing he respected, and built the prep he wished had existed. Not a marketing team that has never sat an exam.

Meet the founder ›Read the values ›

Free forever

Put the formulas to work.

Every formula on this sheet shows up in the free Exam FM question bank, and every question carries a step-by-step solution.

Practice Exam FM questions free →

No credit card. No trial clock.