FORMULAREFERENCEGUIDE
Mathematical formulas and equations used across all calculators. Verify calculations and understand the math behind every result.
Compound Interest
FV = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)]
Variables
- FVFuture Value
- PPrincipal (initial investment)
- rAnnual interest rate (decimal)
- nCompounding periods per year
- tTime in years
- PMTRegular contribution amount
Loan Payment (Amortization)
M = P × [r(1 + r)^n] / [(1 + r)^n - 1]
Variables
- MMonthly payment
- PPrincipal loan amount
- rMonthly interest rate (annual / 12)
- nTotal number of payments
APY (Annual Percentage Yield)
APY = (1 + r/n)^n - 1
Variables
- APYAnnual Percentage Yield
- rNominal annual interest rate (decimal)
- nCompounding periods per year
Simple Interest
I = P × r × t
Variables
- IInterest earned
- PPrincipal amount
- rAnnual interest rate (decimal)
- tTime in years
Mortgage Payment
M = L × [r(1 + r)^n] / [(1 + r)^n - 1] + T/12 + I/12
Variables
- MTotal monthly payment
- LLoan amount (price − down payment)
- rMonthly interest rate
- nTotal payments (years × 12)
- TAnnual property tax
- IAnnual home insurance
Retirement Savings
FV = P(1 + r)^t + C × [((1 + r)^t - 1) / r]
Variables
- FVFuture value at retirement
- PCurrent savings
- rAnnual return rate (decimal)
- tYears until retirement
- CAnnual contribution
Future House Value
FV = PV × (1 + g)^t
Variables
- FVFuture property value
- PVPresent (current) value
- gAnnual growth rate (decimal)
- tTime in years
Credit Card Payoff
n = -log(1 - (B × r)/M) / log(1 + r)
Variables
- nMonths to pay off
- BCurrent balance
- rMonthly interest rate (APR / 12)
- MMonthly payment