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Finance maths cheat sheet

All 9 formulas on one page. Print it or save it as a PDF; it fits on 2 sides of A4 or Letter.

Simple interest

I = Prt

Total amount

A = P(1 + rt)

$I$ the interest earned (or owed)
$P$ the principal: the amount invested or borrowed
$r$ the annual interest rate as a decimal (5% = 0.05; the calculator accepts 5%)
$t$ the time in years

Compound interest

A = P(1 + r/n)^(nt)

Interest earned

I = A − P

Time to reach A

t = (ln (A/P))/(nln (1 + r/n))

$A$ the final amount (principal plus interest)
$P$ the principal: the starting amount
$r$ the nominal annual interest rate as a decimal (6% = 0.06)
$n$ the number of times interest is added per year (1 yearly, 4 quarterly, 12 monthly, 365 daily)
$t$ the time in years

Continuous compounding

A = Pe^(rt)

$A$ the final amount
$P$ the principal (starting amount)
$r$ the annual interest rate as a decimal (5% = 0.05)
$t$ the time in years
$e$ Euler's number, about 2.71828

Effective annual rate

r_eff = (1 + r/n)ⁿ − 1

$r_{eff}$ the effective annual rate (also called AER or APY), as a decimal
$r$ the nominal (stated) annual rate as a decimal (12% = 0.12)
$n$ the number of compounding periods per year

Loan repayment formula

M = Pi/(1 − (1 + i)^( −N)), i = r/k

$M$ the payment each period
$P$ the amount borrowed (principal)
$r$ the annual interest rate as a decimal (6% = 0.06)
$k$ payments per year (12 for monthly)
$N$ the total number of payments (30 years monthly is 360)
$i$ the interest rate per payment period, $r/k$

Present value

PV = FV/((1 + r)^t)

Future value

FV = PV(1 + r)^t

$PV$ the present value: the amount today
$FV$ the future amount
$r$ the interest (discount) rate per period as a decimal
$t$ the number of periods

Future value of an annuity

FV = PMT·((1 + i)^N − 1)/i

$FV$ the future value: the total at the end
$PMT$ the payment made each period (at the end of each period)
$i$ the interest rate per period as a decimal (6% a year paid monthly: 6%/12 = 0.005)
$N$ the number of payments

Present value of an annuity

PV = PMT·(1 − (1 + i)^( −N))/i

$PV$ the present value of all the payments
$PMT$ the payment each period
$i$ the interest rate per period as a decimal
$N$ the number of payments

Rule of 72

t ≈ 72/(100r)

Exact doubling time

t = (ln 2)/(ln (1 + r))

$t$ the approximate number of years to double
$r$ the annual interest rate as a decimal (6% = 0.06), so 100r is the rate in percent

letx.io · Finance maths cheat sheet · 2026-10-31