# Chapter 13: Symbols and Formulas Used

# The Formulas You Need to Know

## Symbols Used

[latex]BAL[/latex] = principal balance immediately after an annuity payment

[latex]BAL_{P1}[/latex] = principal balance immediately prior to the first payment in a series of annuity payments

[latex]BAL_{P2}[/latex] = principal balance immediately after the last payment in a series of annuity payments

[latex]C/Y[/latex] = compounding frequency

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

[latex]INT[/latex] = interest portion of an ordinary single annuity payment or a series of annuity payments

[latex]n[/latex] = number of annuity payments (for annuities) or number of compounding periods (for lump sums)

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

[latex]PRN[/latex] = principal portion of a single annuity payment or a series of annuity payments

[latex]P/Y[/latex] = payment frequency

## Formulas Introduced

Interest Portion of an Ordinary Single Payment:

[latex]INT=BAL \times i[/latex]

Principal Portion of a Single Payment:

$$

[latex]PRN=PMT-INT[/latex]

Principal Portion for a Series of Payments:

[latex]PRN=BAL_{P1}-BAL_{P2}[/latex]

Interest Portion for a Series of Payments:

[latex]INT=N \times PMT - PRN[/latex]