Equations for every formula, including ones that do not have a calculator.
Equal monthly payment on a fixed-rate loan. The rate each month is the annual APR divided by 12.
M = P × [i(1 + i)^n] / [(1 + i)^n − 1]
Future value of a starting balance plus a contribution each compounding period.
FV = P(1 + i)^N + C × [(1 + i)^N − 1] / i
Projected balance from current savings and a monthly contribution, using an effective monthly rate.
FV = P(1 + i)^N + C × [(1 + i)^N − 1] / i
How many months until the balance reaches a target. If the contribution and the return are both zero and you are still short, the goal cannot be reached.
Smallest n where FV(n) ≥ target
Interest charged or earned only on the original principal, not on interest already added.
I = P × r × t
A shortcut that estimates how many years it takes for an amount to double at a fixed annual rate.
Years to double ≈ 72 / annual rate percent
What a future amount is worth today after discounting at an annual rate.
PV = FV / (1 + r)^n
Gain or loss as a percent of the amount you put in.
ROI = (Ending − Invested) / Invested
These formulas are written out here. They do not have a calculator page.
What one amount grows to when it compounds once per year and you add nothing else.
FV = PV × (1 + r)^n
What a series of equal payments grows to, with no starting balance.
FV = PMT × [((1 + r)^n − 1) / r]
What a series of equal future payments is worth today.
PV = PMT × [1 − (1 + r)^(−n)] / r
The effective yearly rate when a nominal APR compounds more than once a year.
APY = (1 + APR / m)^m − 1
The monthly rate that matches a stated annual return. Retirement and savings goal use this rate, not APR ÷ 12.
i = (1 + annual return)^(1/12) − 1
An annual return after removing inflation.
Real return = (1 + nominal) / (1 + inflation) − 1
Growth when interest is compounded continuously.
A = P × e^(r × t)
The steady annual rate that connects a beginning value to an ending value.
CAGR = (Ending / Beginning)^(1 / years) − 1
Monthly debt payments as a share of gross monthly income.
DTI = monthly debt payments / gross monthly income
What you own minus what you owe.
Net worth = assets − liabilities