# Chapter 9: Symbols and Formulas Introduced

# The Formulas You Need to Know

## Symbols Used

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

[latex]C/Y_{\text{New}}[/latex] = The new compounding frequency an interest rate is converted to

[latex]C/Y_{\text{Old}}[/latex] = The old compounding frequency an interest rate is converted from

[latex]FV[/latex] = Future value, or maturity value

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

[latex]i_{\text{New}}[/latex] = The new periodic interest rate after a conversion

[latex]i_{\text{Old}}[/latex] = The old periodic interest rate before a conversion

[latex]I/Y[/latex] = Nominal interest rate per year

[latex]\ln[/latex] = Natural logarithm

[latex]n[/latex] = Number of compound periods

[latex]PV[/latex] = Present value, or principal

## Formulas Introduced

Formula 9.1 Periodic Interest Rate:

[latex]i=\frac{I/Y}{C/Y}[/latex]

Formula 9.2 Number of Compound Periods for Single Payments:

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

Formula 9.3 Compound Interest for Single Payments:

[latex]FV=PV(1+i)^n[/latex]

Formula 9.4 Interest Rate Conversion:

[latex]i_{\text{New}}=(1+i_{\text{Old}})^{\frac{C/Y_{\text{Old}}}{C/Y_{New}}}-1[/latex]