Identify the interest rate type:
Simple interest (constant principal)
Compound interest (interest added to principal)
Simple interest formula:
( I = P times r times t )
Simple interest variables:
( I ) = interest
( P ) = principal
( r ) = annual interest rate (decimal)
( t ) = time in years
Convert rate to decimal if needed:
If ( r % ) is given, use ( r = frac{r%}{100} )
Convert time to years if needed:
Months: ( t = frac{text{months}}{12} )
Days: ( t = frac{text{days}}{365} ) (or use the specified day-count convention)
Simple interest total amount:
( A = P + I )
Compound interest formula (general):
( A = Pleft(1 + frac{r}{n}right)^{nt} )
Compound interest variables:
( A ) = amount
( P ) = principal
( r ) = annual interest rate (decimal)
( n ) = number of compounding periods per year
( t ) = time in years
Compound interest interest earned:
( I = A – P )
If compounding is annual ((n=1)):
( A = P(1+r)^t )
If compounding is monthly ((n=12)):
( A = Pleft(1+frac{r}{12}right)^{12t} )
If compounding is quarterly ((n=4)):
( A = Pleft(1+frac{r}{4}right)^{4t} )
If compounding is continuously (continuous compounding):
( A = Pe^{rt} )
( I = A – P )
For periodic payments/loans (amortized loans), use:
Payment formula:
( text{PMT} = Pcdot frac{r_m(1+r_m)^N}{(1+r_m)^N – 1} )
Variables:
( r_m ) = periodic rate (annual rate divided by number of payments per year)
( N ) = total number of payments
Total interest:
( I = text{PMT}cdot N – P )