5.7 Review, Symbols, and Formulas
key Concepts
5.1: Compound Interest Fundamentals
- How compounding works
- How to calculate the periodic interest rate
5.2: Determining the Future Value
- The basics of taking a single payment and moving it to a future date
- Moving single payments to the future when variables change
5.3: Determining the Present Value
- The basics of taking a single payment and moving it to an earlier date
- Moving single payments to the past when variables change
5.4: Equivalent Payments
- The concept of equivalent payments
- The fundamental concept of time value of money
- The fundamental concept of equivalency
- Applying single payment concepts to loans and payments
5.5: Determining the Interest Rate
- Solving for the nominal interest rate
- How to convert a variable interest rate into its equivalent fixed interest rate
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 5.1 Periodic Interest Rate:
[latex]i=\frac{I/Y}{C/Y}[/latex]
Formula 5.2 Number of Compound Periods for Single Payments:
[latex]n=C/Y \times \text{(Number of Years)}[/latex]
Formula 5.3 Compound Interest for Single Payments:
[latex]FV=PV(1+i)^n[/latex]
Formula 5.4 Interest Rate Conversion:
[latex]i_{\text{New}}=(1+i_{\text{Old}})^{\frac{C/Y_{\text{Old}}}{C/Y_{New}}}-1[/latex]
