8/7/2019 CF Session-4

1/15

Dr. Anubha Gupta

Types of Annuity & Intra year

compounding

8/7/2019 CF Session-4

2/15

Dr. Anubha Gupta

Types of Annuity

The payments or receipts occur at the endof each period for an ordinary annuity whilethey occur at the beginning of each periodfor an annuity due.

8/7/2019 CF Session-4

3/15

Dr. Anubha Gupta

Future Value of an Annuity

Due (Fvad)The Future Value of an Annuity Due is identical

to an ordinary annuity except that each paymentoccurs at the beginning of a period rather than at

the end.

Since each payment occurs one period earlier,we can calculate the future value of an ordinary

annuity and then multiply the result by (1 + i).

8/7/2019 CF Session-4

4/15

Dr. Anubha Gupta

Q. FVAo

What amount will accumulate if we deposit Rs. 5,000 at theend of each year for the next 5 years? Assume an interestof 6% compounded annually.

FVoa = A [(1 + i)n - 1)]i

FVoa = 5,000 [(1.3382255776 - 1) /.06] = 5,000 (5.637092)= 28,185.46Fvoa = A X CVFAFvoa = 5,000 X 5.637 = 28,185.46

8/7/2019 CF Session-4

5/15

Dr. Anubha Gupta

FVadWhat amount will accumulate if we deposit

Rs. 5,000 at the beginning of each year forthe next 5 years? Assume an interest of 6%

compounded annually.FVad = FVoa (1+i)FVad = 28,185.46 (1.06) = 29,876.59

8/7/2019 CF Session-4

6/15

Dr. Anubha Gupta

PVadPvad = PVA X (1+i)

Where,

PVA = A X

PVFA

8/7/2019 CF Session-4

7/15

Dr. Anubha Gupta

Perpetuity Perpetuity is an annuity of indefinite

period.

It may be referred as annuity that neverends.

8/7/2019 CF Session-4

8/15

Dr. Anubha Gupta

Perpetuities & Annuities

PV ofPerpetuity Formula

C = cash paymentr = interest rate

PV=C

r

8/7/2019 CF Session-4

9/15

Dr. Anubha Gupta

Perpetuities & Annuities

Example - Perpetuity

In order to create an endowment, which paysRs. 100,000 per year, forever, how much

money must be set aside today in the rate ofinterest is 10%?

PV=100 , 000

.10=$ 1,000 , 000

8/7/2019 CF Session-4

10/15

8/7/2019 CF Session-4

11/15

Dr. Anubha Gupta

Multiperiod

Compounding

General Formula:FV = PV(1 + [i/m])mn

n: Number of Yearsm: Compounding Periods per Yeari: Annual Interest Rate

FVn,m: FV at the end of Year nPV0: PV of the Cash Flow today

8/7/2019 CF Session-4

12/15

Dr. Anubha Gupta

Frequency of Compounding

ExampleSuppose you deposit Rs. 1,000 in an account

that pays 12% interest, compounded quarterly.

How much will be in the account after two yearsif there are no withdrawals?

PV = Rs. 1,000

i = 12%/4 = 3% per quartern = 2 x 4 = 8 quartersFV = 1000 X (1.03)8

= 1,267

8/7/2019 CF Session-4

13/15

Dr. Anubha Gupta

Real Rate of Interest

1+r=1+ n

1+ ir

Nominal

Interest

Real InterestInflation

8/7/2019 CF Session-4

14/15

Dr. Anubha Gupta

Real

Rate of Interest

The interest on a one-yearTreasury Bill is 18%, expected inflationfor the next year is 9%.

What is the real rate of interest the investordemands?

1 + R = 1 + .18

1 + .091 + R = 1.0825

R = .0825 or 8.25%

8/7/2019 CF Session-4

15/15

Dr. Anubha Gupta

THANK YOU