Ordinary Annuity: Payments or receipts occur at the end of each period

Ordinary Annuity: Payments or receipts occur at the end of each period.

• Ordinary Annuity: Payments or receipts occur at the end of each period.
• Annuity Due: Payments or receipts occur at the beginning of each period.

• An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

• Types of Annuities

Student Loan Payments

• Student Loan Payments
• Car Loan Payments
• Insurance Premiums
• Mortgage Payments
• Retirement Savings

• Examples of Annuities

• 0 1 2 3

• $100 $100 $100

• (Ordinary Annuity)
• End of
• Period 1

• End of
• Period 2

• Today

• Equal Cash Flows
• Each 1 Period Apart

• End of
• Period 3

• Parts of an Annuity

• 0 1 2 3

• $100 $100 $100

• (Annuity Due)
• Beginning of
• Period 1

• Beginning of
• Period 2

• Today

• Equal Cash Flows
• Each 1 Period Apart

• Beginning of
• Period 3

• Parts of an Annuity

FVAn = R(1 + i)n-1 + R(1 + i)n-2 + ... + R(1 + i)1 + R(1 + i)0

• FVAn = R(1 + i)n-1 + R(1 + i)n-2 + ... + R(1 + i)1 + R(1 + i)0

• R R R

• 0 1 2 n n+1

• FVAn

• R = Periodic
• Cash Flow

• Cash flows occur at the end of the period

• i%

• . . .

• Overview of an Ordinary Annuity – FVA

FVA3 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0

• FVA3 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0
• = $1,145 + $1,070 + $1,000 = $3,215

• $1,000 $1,000 $1,000

• 0 1 2 3 4

• $3,215 = FVA3

• 7%

• $1,070

• $1,145

• Cash flows occur at the end of the period

• Example of an Ordinary Annuity – FVA

The future value of an ordinary annuity can be viewed as occurring at the end of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the beginning of the last cash flow period.

• The future value of an ordinary annuity can be viewed as occurring at the end of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the beginning of the last cash flow period.

• Hint on Annuity Valuation

• FVAn = R (FVIFAi%,n) FVA3 = $1,000 (FVIFA7%,3) = $1,000 (3.215) = $3,215

• Valuation Using Table III

• N: 3 Periods (enter as 3 year-end deposits)
• I/Y: 7% interest rate per period (enter as 7 NOT 0.07)
• PV: Not relevant in this situation (no beg value)
• PMT: $1,000 (negative as you deposit annually)
• FV: Compute (Resulting answer is positive)

• N

• I/Y

• PV

• PMT

• FV

• Inputs

• Compute

• 3 7 0 –1,000

• 3,214.90

• Solving the FVA Problem