# 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) = A

_{0}(1 + r/n)

^{nt}

A(t) : Amount function

A

_{0}: 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