Free GARP FRM Part I Formula Sheet (2026)

Every FRM Part I formula you need on the test, grouped by topic and rendered with full math notation. 84 formulas across 4 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

84 formulas 4 topics 2026 syllabus Free forever
Print-ready PDF: 1080x1350 portrait, math pre-rendered, fonts embedded. Download once, study anywhere.
Download PDF →

All FRM Part I Formulas

Foundations of Risk Management 12 items
Annual CDS premium payment
Premium=s×N\text{Premium} = s \times N
s = CDS spread (decimal), N = notional protected. Example: 250 bps on $800M = $20M/year
Expected loss on a credit exposure
EL=PD×LGD×EADEL = PD \times LGD \times EAD
PD = probability of default, LGD = loss given default, EAD = exposure at default
CAPM expected return
E[Ri]=Rf+βi(E[Rm]−Rf)E[R_i] = R_f + \beta_i (E[R_m] - R_f)
RfR_f = risk-free rate, βiβ_i = asset beta, E[RmR_m] = expected market return
CDS spread approximation
s≈PD×LGDs \approx PD \times LGD
s = annualized CDS spread, PD = annual probability of default, LGD = loss given default (1 − recovery)
Beta of an asset
βi=Cov(Ri,Rm)σm2\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2}
Cov(R_i,RmR_m) = covariance of asset and market returns, σmσ_m² = market return variance
Jensen's alpha
α=Rˉp−[Rf+βp(Rˉm−Rf)]\alpha = \bar R_p - [R_f + \beta_p(\bar R_m - R_f)]
R̄_p = realized portfolio return, RfR_f = risk-free rate, βpβ_p = portfolio beta, R̄_m = market return
Aggregate firm-wide economic capital variance
σfirm2=∑iσi2+2∑i<jρijσiσj\sigma_{firm}^2 = \sum_i \sigma_i^2 + 2\sum_{i<j} \rho_{ij}\sigma_i\sigma_j
σiσ_i = standalone EC of silo i, ρijρ_{ij} = pairwise correlation between silos i and j
Factor model return decomposition
Ri=E[Ri]+βi,1f1+⋯+βi,kfk+εiR_i = E[R_i] + \beta_{i,1}f_1 + \cdots + \beta_{i,k}f_k + \varepsilon_i
fkf_k = zero-mean factor surprise, βi,kβ_{i,k} = factor loading, εiε_i = idiosyncratic noise
Risk-adjusted return on capital (RAROC)
RAROC=Risk-adjusted returnEconomic capitalRAROC = \dfrac{\text{Risk-adjusted return}}{\text{Economic capital}}
numerator = return net of EL and funding costs, denominator = economic capital allocated
Fama-French three-factor model
E[Ri]−Rf=βi,M(RM−Rf)+βi,SMB⋅SMB+βi,HML⋅HMLE[R_i] - R_f = \beta_{i,M}(R_M - R_f) + \beta_{i,SMB}\cdot SMB + \beta_{i,HML}\cdot HML
RMR_M = market return, SMB = small minus big, HML = high minus low book-to-market
APT multifactor expected return
E[Ri]=Rf+βi,1λ1+βi,2λ2+⋯+βi,kλkE[R_i] = R_f + \beta_{i,1}\lambda_1 + \beta_{i,2}\lambda_2 + \cdots + \beta_{i,k}\lambda_k
RfR_f = risk-free rate, βi,kβ_{i,k} = asset i loading on factor k, λkλ_k = factor k risk premium
Treynor ratio
T=Rp−RfβpT = \dfrac{R_p - R_f}{\beta_p}, excess return per unit of systematic risk (beta). Preferred over the Sharpe ratio for ranking well-diversified sub-portfolios where idiosyncratic risk is already diversified away.
Quantitative Analysis 23 items
AR(1) mean-reverting level
μ=α1−ϕ\mu = \dfrac{\alpha}{1 - \phi}
α = intercept, φ = AR(1) coefficient with |φ| < 1, μ = unconditional long-run mean
Continuously compounded (log) return
r=ln⁡(Pt/Pt−1)=ln⁡(1+R)r = \ln(P_t / P_{t-1}) = \ln(1 + R)
PtP_t = price at time t, Pt−1P_{t-1} = prior price, R = simple return over the period
Sample variance with Bessel's correction
s2=1n−1∑i=1n(Xi−Xˉ)2s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2
XiX_i = observation i, Xˉ\bar{X} = sample mean, n = sample size
Bayes' rule
P(A∣B)=P(B∣A) P(A)P(B)P(A \mid B) = \dfrac{P(B \mid A) \, P(A)}{P(B)}; P(A) = prior, P(B|A) = likelihood, P(B) = marginal evidence = P(B|A)P(A) + P(B|Aᶜ)P(Aᶜ)
Expected value of a lognormal random variable
E[X]=eμ+σ2/2E[X] = e^{\mu + \sigma^2/2}
μ = mean of ln(X), σ² = variance of ln(X); the σ²/2 is the convexity adjustment
F1 score for binary classification
F1=2⋅P⋅RP+RF_1 = \frac{2 \cdot P \cdot R}{P + R}
P = precision = TP/(TP+FP), R = recall = TP/(TP+FN), TP/FP/FN from confusion matrix
Law of total probability (two-event partition)
P(B)=P(B∣A)P(A)+P(B∣Ac)P(Ac)P(B) = P(B \mid A) P(A) + P(B \mid A^c) P(A^c)
A and A^c partition the sample space, P(B|·) = conditional probability of B
Adjusted R-squared
Rˉ2=1−(1−R2)⋅n−1n−k−1\bar{R}^2 = 1 - (1 - R^2) \cdot \frac{n - 1}{n - k - 1}
R² = unadjusted R-squared, n = sample size, k = number of regressors
OLS slope estimator (single regressor)
β^1=Cov(X,Y)Var(X)\hat{\beta}_1 = \frac{\text{Cov}(X, Y)}{\text{Var}(X)}
Cov(X,Y) = sample covariance of X and Y, Var(X) = sample variance of X
AR(1) h-step-ahead forecast
E[Yt+h]=μ+ϕh(Yt−μ)E[Y_{t+h}] = \mu + \phi^h (Y_t - \mu)
μ = mean-reverting level, φ = AR coefficient, h = forecast horizon, YtY_t = current value
Pearson correlation coefficient
ρX,Y=Cov(X,Y)σXσY\rho_{X,Y} = \dfrac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}
Cov = covariance of X and Y; σXσ_X, σYσ_Y = standard deviations; ρ ∈ [-1, 1]
Square-root-of-time volatility scaling
σT=σ1T\sigma_T = \sigma_1 \sqrt{T}
σTσ_T = T-period volatility, σ1σ_1 = one-period volatility, T = number of periods (assumes iid returns)
Variance of a linear transformation
Var(aX+b)=a2 Var(X)\text{Var}(aX + b) = a^2 \, \text{Var}(X)
X = random variable, a = scale factor, b = shift constant
Omitted variable bias in a short regression coefficient
bias(β^1)=β2⋅δ\text{bias}(\hat{\beta}_1) = \beta_2 \cdot \delta
β₂ = true coefficient on omitted X₂, δ = slope from regressing X₂ on included X₁
Variance of a two-asset weighted sum
Var(aX+bY)=a2σX2+b2σY2+2ab Cov(X,Y)\text{Var}(aX + bY) = a^2 \sigma_X^2 + b^2 \sigma_Y^2 + 2ab\,\text{Cov}(X,Y)
a, b = weights; σ = standard deviation; Cov = covariance
Variance inflation factor for regressor j
VIFj=11−Rj2\text{VIF}_j = \frac{1}{1 - R_j^2}
R²_j = R-squared from regressing XjX_j on the other regressors; VIF > 10 commonly flags collinearity
One-sample t-statistic for testing a mean
t=Xˉ−μ0s/nt = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}
Xˉ\bar{X} = sample mean, μ0\mu_0 = hypothesized mean, s = sample std dev, n = sample size
Box-Pierce Q-statistic for residual autocorrelation
QBP=T∑k=1mρ^k2Q_{BP} = T \sum_{k=1}^{m} \hat{\rho}_k^2
T = sample size, m = number of lags tested, ρ̂_k = sample autocorrelation of residuals at lag k
LASSO regression penalized objective
min⁡β∑i(yi−y^i)2+λ∑j∣βj∣\min_\beta \sum_i (y_i - \hat{y}_i)^2 + \lambda \sum_j |\beta_j|
yiy_i = observed, ŷ_i = predicted, βjβ_j = coefficient j, λ = L1 penalty strength
Ridge regression penalized objective
min⁡β∑i(yi−y^i)2+λ∑jβj2\min_\beta \sum_i (y_i - \hat{y}_i)^2 + \lambda \sum_j \beta_j^2
yiy_i = observed, ŷ_i = predicted, βjβ_j = coefficient j, λ = L2 penalty strength
Two-sample t-statistic for difference of means
t=Xˉ1−Xˉ2s12/n1+s22/n2t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}
Xˉi\bar{X}_i = sample mean i, sis_i = sample std dev i, nin_i = sample size i
Jarque-Bera test statistic
JB=n6[S2+(K−3)24]JB = \frac{n}{6}\left[S^2 + \frac{(K-3)^2}{4}\right]
n = sample size, S = sample skewness, K = sample kurtosis; chi-square with 2 dof under normality
F-statistic for joint hypothesis test
F=(RSSR−RSSU)/qRSSU/(n−k−1)F = \frac{(\text{RSS}_R - \text{RSS}_U) / q}{\text{RSS}_U / (n - k - 1)}
RSSRRSS_R = restricted RSS, RSSURSS_U = unrestricted RSS, q = restrictions, n = sample, k = regressors
Financial Markets and Products 26 items
European call lower bound (no dividend)
c≥max⁡(S0−Ke−rT,  0)c \geq \max(S_0 - K e^{-rT},\; 0)
c = call price, S₀ = spot, K = strike, r = risk-free rate, T = time to maturity
European put lower bound (no dividend)
p≥max⁡(Ke−rT−S0,  0)p \geq \max(K e^{-rT} - S_0,\; 0)
p = put price, K = strike, r = risk-free rate, T = time to maturity, S₀ = spot
Continuous-to-discrete compounding conversion
Rc=mln⁡(1+Rm/m)R_c = m \ln(1 + R_m/m)
RcR_c = continuous rate, RmR_m = rate compounded m times per year, m = compounding frequency
Bull call spread maximum profit
Max profit=K2−K1−D\text{Max profit} = K_2 - K_1 - D
K1K_1 = long (lower) call strike, K2K_2 = short (higher) call strike, D = net debit paid
Optimal number of futures contracts (untailed)
N∗=h∗⋅QA/QFN^* = h^* \cdot Q_A / Q_F
h* = optimal hedge ratio, QAQ_A = size of cash exposure, QFQ_F = futures contract size
Cost-of-carry forward price for a commodity
F0=S0e(r+u−y)TF_0 = S_0 e^{(r+u-y)T}
S₀ = spot, r = risk-free rate, u = storage cost rate, y = convenience yield, T = time to delivery
Forward price on a non-income asset
F0=S0erTF_0 = S_0 e^{rT}
S₀ = spot price, r = continuously compounded risk-free rate, T = time to delivery in years
Relative purchasing power parity
(S1−S0)/S0≈id−if(S_1 - S_0)/S_0 \approx i_d - i_f
S0S_0 = current spot, S1S_1 = future spot, idi_d = domestic inflation, ifi_f = foreign inflation
Put-call parity for European options (no dividend)
c+Ke−rT=p+S0c + K e^{-rT} = p + S_0
c = call price, p = put price, K = strike, r = risk-free rate, T = time to maturity, S₀ = spot price
Long straddle breakeven prices
S∗=K±(c+p)S^* = K \pm (c + p)
K = common strike, c = call premium, p = put premium; profit if |S(T) − K| > c + p
Bond price change with duration and convexity
ΔP/P≈−DmodΔy+12C(Δy)2\Delta P/P \approx -D_{mod} \Delta y + \tfrac{1}{2} C (\Delta y)^2
DmodD_{mod} = modified duration, C = convexity, Δy = yield change
Uncovered interest rate parity expected future spot
E[ST]=S⋅(1+rd)/(1+rf)E[S_T] = S \cdot (1 + r_d) / (1 + r_f)
E[STS_T] = expected future spot, S = current spot, rdr_d = domestic rate, rfr_f = foreign rate
Conditional prepayment rate from single monthly mortality
CPR=1−(1−SMM)12CPR = 1 - (1 - SMM)^{12}
SMM = single monthly mortality, CPR = annualized conditional prepayment rate
Forward price with continuous income yield
F0=S0e(r−q)TF_0 = S_0 e^{(r-q)T}
S₀ = spot, r = risk-free rate, q = continuous income yield (dividend or foreign rate), T = time to delivery
Modified duration from Macaulay duration
Dmod=DMac/(1+y/m)D_{mod} = D_{Mac} / (1 + y/m)
DMacD_{Mac} = Macaulay duration, y = yield, m = compounding periods per year
Cheapest-to-deliver delivery cost
Cost=Quoted price−(F×CF)\text{Cost} = \text{Quoted price} - (F \times CF)
Quoted price = clean bond price, F = futures settlement, CF = conversion factor
Tailed number of futures contracts
Ntailed∗=h∗⋅VA/VFN^*_{\text{tailed}} = h^* \cdot V_A / V_F
VAV_A = QAQ_A × S (dollar value of exposure), VFV_F = QFQ_F × F (dollar value of one futures contract)
Number of index futures to adjust portfolio beta
N∗=(β∗−β0)⋅P/FN^* = (\beta^* - \beta_0) \cdot P / F
β* = target beta, β0β_0 = current portfolio beta, P = portfolio value, F = index futures contract value
Covered interest rate parity forward rate
F=S⋅(1+rd)/(1+rf)F = S \cdot (1 + r_d) / (1 + r_f)
F = forward rate, S = spot, rdr_d = domestic interest rate, rfr_f = foreign interest rate (matched to horizon)
Duration-based futures hedge ratio
N∗=P⋅DPVF⋅DFN^* = \frac{P \cdot D_P}{V_F \cdot D_F}
P = portfolio value, DPD_P = portfolio duration, VFV_F = futures contract value, DFD_F = CTD bond duration
Swap value to fixed-receiver (two-bond method)
V=Bfix−BflV = B_{\text{fix}} - B_{\text{fl}}
BfixB_{fix} = PV of fixed-rate bond (coupons + notional), BflB_{fl} = PV of floating-rate bond (next coupon + notional)
Fisher relation linking nominal and real rates
(1+r)=(1+ρ)(1+i)(1 + r) = (1 + \rho)(1 + i)
r = nominal rate, ρ = real rate, i = expected inflation
Long forward payoff at maturity
Payoff=ST−K\text{Payoff} = S_T - K
STS_T = spot price at maturity, K = forward strike price
Variance swap payoff at maturity
Payoff=Nvar×(σrealized2−Kvar2)\text{Payoff} = N_{var} \times (\sigma_{realized}^2 - K_{var}^2)
NvarN_{var} = variance notional, σ²_realized = realized variance, KvarK_{var} = strike volatility
Long put option payoff at maturity
Payoff=max⁡(K−ST,0)\text{Payoff} = \max(K - S_T, 0)
K = strike price, STS_T = spot at maturity
FRA settlement payment
Payment=N (rref−rFRA) (d/360)1+rref (d/360)\text{Payment} = \dfrac{N\,(r_{ref} - r_{FRA})\,(d/360)}{1 + r_{ref}\,(d/360)}, settled at the start of the reference period. N = notional, d = day count, rrefr_{ref} = reference rate.
Valuation and Risk Models 23 items
Forward rate between two dates (continuous compounding)
f(t1,t2)=s2t2−s1t1t2−t1f(t_1, t_2) = \frac{s_2 t_2 - s_1 t_1}{t_2 - t_1}
s1, s2 = spot rates to t1 and t2, f = forward rate from t1 to t2
Black-Scholes-Merton call price (no dividends)
C=S0N(d1)−Ke−rTN(d2)C = S_0 N(d_1) - K e^{-rT} N(d_2)
S₀ = spot, K = strike, r = risk-free rate, T = maturity, N = standard normal CDF
Cox-Ross-Rubinstein up and down factors
u=eσΔt, d=1/uu = e^{\sigma \sqrt{\Delta t}},\ d = 1/u
σ = annualized volatility of the underlying, Δt = step length in years
BSM gamma for a European option (no dividends)
Γ=ϕ(d1)/(S0σT)\Gamma = \phi(d_1) / (S_0 \sigma \sqrt{T})
φ = standard normal density, S₀ = spot, σ = volatility, T = maturity
d₁ in the Black-Scholes-Merton formula (no dividends)
d1=ln⁡(S0/K)+(r+σ2/2)TσTd_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}
S₀ = spot, K = strike, r = rate, σ = volatility, T = maturity
Unexpected loss on a single credit exposure (binomial default)
UL=EAD×LGD×PD(1−PD)UL = EAD \times LGD \times \sqrt{PD(1-PD)}
EAD = exposure at default, LGD = loss given default, PD = probability of default
Risk-neutral probability in a binomial tree
p=erΔt−du−dp = \frac{e^{r \Delta t} - d}{u - d}
r = risk-free rate, Δt = step length, u = up-factor, d = down-factor
Unconditional default probability under constant hazard rate
P(τ≤t)=1−e−λtP(\tau \le t) = 1 - e^{-\lambda t}
λ = constant hazard rate (annual default intensity), t = horizon in years, τ = default time
KR01 from key-rate duration
KR01k=KRDk⋅P⋅10−4\text{KR01}_k = \text{KRD}_k \cdot P \cdot 10^{-4}
KRDkKRD_k = key-rate duration at rate k, P = bond price; dollar change per 1 bp shift
Survival probability under constant hazard rate
P(τ>t)=e−λtP(\tau > t) = e^{-\lambda t}
λ = constant hazard rate, t = horizon in years, τ = default time
Bond price from discount factors
P=∑i=1nc⋅d(ti)+P⋅d(tn)P = \sum_{i=1}^{n} c \cdot d(t_i) + P \cdot d(t_n)
c = coupon, P = principal, d(t) = discount factor for time t, n = number of payments
Basel total market-risk capital with stressed VaR
K=max⁡(VaR,VaR‾60d)+max⁡(sVaR,sVaR‾60d)K = \max(VaR, \overline{VaR}_{60d}) + \max(sVaR, \overline{sVaR}_{60d})
VaR = current VaR, sVaR = stressed VaR, 60d-bar = 60-day average
Expected Shortfall under normal returns
ESc=μ+σ⋅ϕ(zc)1−c\text{ES}_c = \mu + \sigma \cdot \frac{\phi(z_c)}{1-c}
μ = mean, σ = std dev, φ(z_c) = standard-normal density at zcz_c, c = confidence level
Effective duration from shocked prices
Deff=P−−P+2P0ΔyD_{\text{eff}} = \frac{P_- - P_+}{2 P_0 \Delta y}
P₋ = price after yield drop, P₊ = price after yield rise, P₀ = base price, Δy = shock size
Parametric (delta-normal) VaR
VaRc=−μ+zcσ\text{VaR}_c = -\mu + z_c \sigma
μ = expected return, σ = return standard deviation, zcz_c = one-sided standard-normal quantile at confidence c
Loss given default from recovery rate
LGD=1−RR\text{LGD} = 1 - \text{RR}
LGD = loss given default (fraction of exposure lost), RR = recovery rate (fraction of par recovered after default)
Macaulay duration
Dmac=∑i=1nti⋅PV(Ci)PD_{\text{mac}} = \sum_{i=1}^{n} t_i \cdot \frac{PV(C_i)}{P}
tit_i = time to cash flow i, PV(C_i) = present value of cash flow i, P = bond price
Effective annual rate from nominal rate
EAR=(1+r/n)n−1\text{EAR} = (1 + r/n)^n - 1
r = nominal annual rate, n = compounding periods per year
Dollar value of an 01 (DV01)
DV01≈Dmod×P×10−4\text{DV01} \approx D_{\text{mod}} \times P \times 10^{-4}
DmodD_{mod} = modified duration, P = bond price; dollar price change for a 1 bp yield change
GARCH(1,1) variance recursion
σt2=ω+αrt−12+βσt−12\sigma_t^2 = \omega + \alpha r_{t-1}^2 + \beta \sigma_{t-1}^2
ω = constant, α = ARCH weight on lagged squared return, β = GARCH weight on lagged variance
Conditional one-year default probability given survival
P(default in next year∣survived)=1−e−λP(\text{default in next year} \mid \text{survived}) = 1 - e^{-\lambda}
λ = constant annual hazard rate; value is the same each year under constant intensity
Vasicek single-factor credit VaR (Basel IRB)
VaRc=Φ(Φ−1(PD)+ρ Φ−1(c)1−ρ)VaR_c = \Phi\left(\frac{\Phi^{-1}(PD) + \sqrt{\rho}\,\Phi^{-1}(c)}{\sqrt{1-\rho}}\right)
PD = default probability, ρ = asset correlation, c = confidence level, Φ = standard-normal CDF
Option vega
ν=∂V∂σ\nu = \dfrac{\partial V}{\partial \sigma}, the change in option value per one-point change in volatility. Positive for long calls and puts; largest for at-the-money options with longer time to maturity.
Take the free FRM Part I diagnostic quiz →
Instant readiness score in about 6 minutes. No signup to start.

Frequently Asked Questions

Is the FRM Part I formula sheet free?
Yes. The full FRM Part I formula sheet is free, with no signup, no email, and no credit card required. 84 formulas across 4 topics, all rendered with the same KaTeX math notation used in the FreeFellow study app.
Can I download the FRM Part I formula sheet as a printable PDF?
Yes. A 1080x1350 portrait PDF (Instagram and LinkedIn carousel native size, also great for tablet study) is linked at the top of this page. The PDF is fully self-contained: math is pre-rendered, fonts are embedded, no internet connection needed once downloaded.
What's covered on the FRM Part I formula sheet?
Every formula is grouped by official syllabus topic, with the formula in math notation plus a one-line note on when to use it (or a watch-out from CAIA, CFA, or other prep-provider commentary). Coverage is calibrated to the 2026 syllabus and refreshed when the corpus changes.
What is FreeFellow's relationship with GARP?
No. FreeFellow is not affiliated with GARP. GARP does not endorse, promote, review, or warrant the accuracy of the products or services offered by FreeFellow LLC.
What else is free at FreeFellow for FRM Part I candidates?
The full original question bank is free with an account, subject to usage limits. Worked solutions, written lessons, mixed practice, and your readiness score stay free. The formula sheet is free too. Fellow is $39 per month or $79 per quarter, per exam family (USD). Fellow Plus is $49 per month, $99 per quarter, or $199 per year, per exam family (USD). Every annual plan is Fellow Plus. Fellow adds timed mock exams, spaced-repetition flashcards, performance analytics, and a personalized study plan.

Formula sheets for other exams

Exam P Exam FM Exam FAM Exam SRM Exam PA Exam ALTAM Exam ASTAM CFA Level I CFA Level II CFA L3 Portfolio Mgmt CFA L3 Private Wealth CFA L3 Private Markets

About FreeFellow

Jeffrey Ting, founder of FreeFellow
Jeffrey Ting
FSA, CFA · Founder

FreeFellow was built by Jeffrey Ting, a credentialed actuary and CFA charterholder who has passed thirteen of the hardest exams in finance, all on his first attempt. He paid four-figure prep fees along the way.

So he started writing his own questions, then lessons, then mock exams, until it grew into a full prep platform covering 40 exams with more than 45,000 original practice questions.

01
Cost shouldn't decide who gets in.

A CFA charter, a CPA license, an actuarial credential. Each opens a real career, but prep fees add to the cost of getting there. FreeFellow keeps its original question bank and written lessons free so you can study even if a paid course is out of reach.

02
Free should mean free.

The original question bank, the worked solutions, the topic lessons, mixed practice, and your readiness score stay free, forever. Full access needs a free account, and practice usage limits apply. Fellow adds AI grading on supported exams, spaced-repetition flashcards, full-length mock exams, analytics, and a study plan that adapts to your progress.

Meet the founder ›Read the values ›

Free forever

Put the formulas to work.

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

Practice FRM Part I questions free →

No credit card. No trial clock.