7.8 Review, Symbols, and Formulas
key Concepts
Fundamentals of Annuities
- Understanding what an annuity is
- The four different types of annuities
- The difference between annuities and single payments
- The annuity timeline format
Future Value of Annuities
- The future value of ordinary annuities
- Variable changes in future value annuity calculations
- The future value of annuities due
Present Value of Annuities
- The present value of both ordinary annuities and annuities due
- Variable changes in present value annuity calculations
- Applying both future value and present value calculations to loans
- Determining loan balances
- Selling loan contracts between companies
Annuity Payment Amounts
- Calculating the annuity payment amount for both ordinary annuities and annuities due
Number of Annuity Payments
- Calculating the number of annuity payments (term) for both ordinary annuities and annuities due
- What to do when N has decimals
Annuity Interest Rates
- Calculating the interest rate for both ordinary annuities and annuities due
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]
