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

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## 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
• 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
• 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
• 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
• 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

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