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Money & Business formula solvers

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Loan Payment (Amortized Loan or Mortgage)

M=P i1−(1+i)−nM = \frac{P\,i}{1 - (1+i)^{-n}}

Money & BusinessLevel payment that retires a loan of principal P in exactly n payments at periodic interest rate i — the mortgage, truck loan and equipment finance formula.

Total Interest Paid Over a Loan

I=M n−PI = M\,n - P

Money & BusinessEverything a loan costs beyond the amount borrowed: total of all payments minus the principal.

Future Value of an Annuity (Regular Deposits)

FV=D (1+i)n−1i\mathit{FV} = D\,\frac{(1+i)^n - 1}{i}

Money & BusinessWhat an equal deposit made at the end of every period grows to after n periods at rate i — the replacement-fund and savings-plan formula.

Simple Payback Period

t=CSt = \frac{C}{S}

Money & BusinessYears for an upgrade to repay its own capital cost out of the money it saves each year, ignoring interest and inflation.

Return on Investment (ROI)

ROI=G−CC\mathit{ROI} = \frac{G - C}{C}

Money & BusinessProfit expressed as a fraction of what was spent: total value returned minus cost, divided by cost.

Straight-Line Depreciation

D=C−SnD = \frac{C - S}{n}

Money & BusinessEqual annual write-down of an asset: cost minus salvage value, spread evenly over its useful life.

Declining-Balance Depreciation (Book Value)

B=C (1−d)kB = C\,(1 - d)^k

Money & BusinessBook value of an asset after k years when a fixed fraction d of the remaining value is written off every year.

Markup Percentage (on Cost)

m=P−CCm = \frac{P - C}{C}

Money & BusinessMarkup states profit as a fraction of what the item COST you. A 25% markup on an $80 cost gives a $100 price.

Gross Margin Percentage (on Price)

g=P−CPg = \frac{P - C}{P}

Money & BusinessMargin states the same profit as a fraction of the SELLING PRICE. The $80 cost sold at $100 is a 20% margin, not 25% — the classic small-business mix-up.

Markup and Margin Conversion

m=g1−gm = \frac{g}{1 - g}

Money & BusinessConverts directly between markup on cost and gross margin on price. A 50% markup is a 33.3% margin; a 20% margin is a 25% markup.

Break-Even Quantity

Q=Fp−vQ = \frac{F}{p - v}

Money & BusinessUnits that must be sold before fixed costs are covered: fixed cost divided by the contribution margin, price minus variable cost per unit.

Sales Tax and Total Price

T=P (1+r)T = P\,(1 + r)

Money & BusinessTotal payable from a pre-tax price and a tax rate, and the reverse: recovering the pre-tax price from a tax-inclusive total.

Discount Price (Percentage Off)

S=L (1−d)S = L\,(1 - d)

Money & BusinessPrice after a percentage is taken off the list price, and the discount implied by any pair of list and sale prices.

Effective Annual Rate from a Nominal Rate

EAR=(1+rm)m−1\mathit{EAR} = \left(1 + \frac{r}{m}\right)^{m} - 1

Money & BusinessWhat a quoted nominal annual rate really costs or earns once it compounds m times a year — 12% compounded monthly is 12.68% effective.

Real Interest Rate (Fisher Equation)

rreal=1+i1+f−1r_{\text{real}} = \frac{1 + i}{1 + f} - 1

Money & BusinessWhat a return is worth after inflation is taken out, done exactly rather than by the rough subtraction that overstates it.

Rule of 72 (Doubling Time)

n≈0.72in \approx \frac{0.72}{i}

Money & BusinessMental-arithmetic estimate of how many periods it takes money to double at rate i — with the rate written as a percentage R, it is the familiar 72 divided by R.