# Chapter 11: Symbols and Formulas Introduced

# The Formulas You Need to Know

## Symbols Used

[latex]C/Y[/latex] = compounding per year or compounding frequency

[latex]FV_{Due}[/latex] = future value of annuity due

[latex]FV_{Ord}[/latex] = future value of an ordinary annuity

[latex]I/Y[/latex] = nominal interest rate

[latex]i[/latex] = periodic interest rate

[latex]i[/latex] = number of annuity payments

[latex]P/Y[/latex] = payments per year or payment frequency

[latex]PMT[/latex] = annuity payment amount

[latex]PV_{Due}[/latex] = present value of annuity due

[latex]PV_{Ord}[/latex] = present value of ordinary annuity

[latex]Years[/latex] = the term of the annuity

## Formulas Introduced

Number of Annuity Payments:

[latex]n=P/Y \times \text{(Number of Years)}[/latex]

Ordinary Annuity Future Value:

[latex]FV_{ORD}=PMT \left[\frac{(1+i)^n-1}{i}\right][/latex]

Annuity Due Future Value:

[latex]FV_{DUE}=PMT \left[\frac{(1+i)^n-1}{i}\right]\times(1+i)[/latex]

Ordinary Annuity Present Value:

[latex]PV_{ORD}=PMT \left[\frac{1-(1+i)^{-n}}{i}\right][/latex]

Annuity Due Present Value:

[latex]PV_{DUE}=PMT \left[\frac{1-(1+i)^{-n}}{i}\right] \times(1+i)[/latex]