Interest Formulas

Simplified Interest Calculations

To find the future value of an interest problem, the formula is as follows:

FV = PV(1 + i)ⁿ

FV : Future Value
PV : Present Value
i : Interest rate
n : Number of periods

To solve a problem seeking the PV of an interest problem, the formula is as follows:

PV = FV ÷(1 + i)ⁿ

PV : Present Value
FV : Future Value
i : Interest Rate
n : Number of periods

To solve for i in an interest problem, the formula is:

i = (FV / PV)^1/n-1

i : Interest Rate
FV : Future Value
PV : Present Value
n : Number of periods

To solve for n, number of periods, for an interest problem, the formula is:

n = log(FV) - log(PV) ÷ log(1 - i)

n : Number of periods
FV : Future Value
PV : Future Value
i : Interest rate

Compound Interest Formula

To solve for a compound interest problem, the formula is:

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

A : Final Amount
P : Principal(Initial Investment)
r : Interest Rate(as a decimal; i.e. 6 is .06)
n : Number of times interest is compounded (1=annual,2=semi-annual,4=quarterly)
t : Number of periods; time

Periodic Interest

To solve for periodic interest problems, the formula is:
A(t) = A₀(1 + r/n)^nt

A(t) : Amount function
A₀ : Coefficient
t : Total time in years
n : Number of compounding periods per year
r : Nominal interest rate (6% is .06)

Continuous Compound Interest Formula

To solve a problem seeking continuous compound interest, the formula is:
A = Pe^rt


where,
A = Amount of future value
P = Initial amount invested
e = Stands for Napier's number and is approximately 2.7183
r = Interest rate
t = Length of time investment will accrue