1. Chapter 1 Annuities Dr. A. PHILIP AROKIADOSS Assistant Professor
Students Are Smart!
Chapter 1 Annuities
Dr. A. PHILIP AROKIADOSS
Assistant Professor
Department of Statistics
St. Joseph’s College (Autonomous)
Tiruchirappalli
Finance Is Fun!

2. Annuities Equal Cash Flows at Equal Time Intervals
Ordinary Annuity (End): Cash Flow At End Of Each Period
Annuity Due (Begin): Cash Flow At Beginning Of Each Period
Examples:
Savings Plan: Save $50 at the end of each month
Savings Plan: How Much Do I have to put in bank each month for 35 years to become a millionaire?
Borrow Money: What is my monthly payment if I borrow $190,000?
Asset Valuation: How much should I pay for a machine if it will yield Cash Flow of $10,000 at the each of each year for the next 15 years?

3. Annuities Annuity Definition: Timing for annuities:
A level steam of cash flows for a fixed period of time
Each payment is for the same amount
Payments are referred to as: PMT
The time between PMT is always the same
Timing for annuities:
Ordinary Annuity (Savings Plans, Mortgage contracts)
PMT are made at the end of each period
The day you sign the contract, you do not make a PMT
Annuity due (Lease contracts)
PMT are made at the beginning of each period

4. Types of Annuities Savings plan:
If I put $50 (PMT) in the bank at the end of each month for 50 years, how much will I have when I retire? What is the future value?
Future value of future cash flows valuation:
If I want to be a millionaire, how much do I have to put in the bank at the end of each month. What is the PMTFV?
Loan (DEBT) periodic payment:
If I take out a loan for $190,000, what is the monthly payment amount paid at the end of each month (PMT)? What is the PMTPV?
Present value of future cash flows valuation
If I know the asset will give me $10,000 (PMT) at the end of each year for the next 15 years, what should I pay for this asset today? What is the present value?

5. Math Book Formulas Ordinary Annuity (End):

6. Math Book Formulas Ordinary Annuity (End):

7. Variables

8. FV & PMTFV for for Ordinary Annuity (End)
Excel Functions:
FV (Savings Plan) =FV(rate , nper , -PMT) PMT (Savings Plan) =PMT(rate , nper , , FV) **Skip PV arguments (put 2 commas) ** If you put –PV in, it just means you had so $ in bank to start…
Math Formulas:
FV =PMT*((1+i/n)^(x*n)-1)/(i/n) PMT =FV/(((1+i/n)^(x*n)-1)/(i/n))

9. FV & PMTFV for Annuity Due (Begin)
Excel Functions:
FV (Savings Plan) =FV(rate , nper , -PMT , , 1) PMT (Savings Plan) =PMT(rate , nper , , FV , 1) **Skip PV arguments (put 2 commas) ** If you put –PV in, it just means you had so $ in bank to start…
Math Formulas:
FV =PMT*((1+i/n)^(x*n)-1)/(i/n)*(1+i/n) PMT =FV/(((1+i/n)^(x*n)-1)/(i/n))/(1+i/n)

10. PV & PMTPV for Ordinary Annuity (End)
Students Are Smart!
PV & PMTPV for Ordinary Annuity (End)
Excel Functions:
PMT (Borrower Loan) =PMT(rate , nper , PV) **PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out) PV (Asset Valuation) =PV(rate , nper , PMT) **PMT positive cuz cash come into business, PV negative cuz that is max you should pay for asset
Math Formulas:
PMT =PV/(((1+i/n)^-(x*n)-1)/(i/n)) PV =PMT*((1+i/n)^-(x*n)-1)/(i/n)
Finance Is Fun!

11. PV & PMTPV for Annuity Due (Begin)
Excel Functions:
PMT (Borrower Loan) =PMT(rate , nper , PV, ,1) **Skip FV arguments (put 2 commas) **PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out) PV (Asset Valuation) =PV(rate , nper , PMT, ,1) **PMT positive cuz cash come into business, PV negative cuz that is max you should pay for asset
Math Formulas:
PMT =PV/(((1+i/n)^-(x*n)-1)/(i/n))/(1+i/n) PV =PMT*((1+i/n)^-(x*n)-1)/(i/n)*(1+i/n)

12. PMTPV for Ordinary Annuity (End)
Excel Functions:
PMT (Withdraw During Retirement) =PMT(rate , nper , -PV) **PV negative cuz you put $ in bank, PMT positive cuz you get money in each period