An annuity is a series of fixed payments made over a specified period of time, with common payment frequencies being yearly, semi-annually, quarterly, and monthly. The present value of an annuity is the current worth of future cash flows discounted at a given interest rate, with a higher discount rate resulting in a lower present value. The future value is the amount one would have in the future given a specified interest rate, with a higher discount rate yielding a higher future value. Annuities can be ordinary, with payments at the end of each period, or annuities due, with payments at the beginning of each period.

1. Annuity

2. What are Annuities?
 Essentially a series of fixed payments
 Required from a person or paid to a
person at a specified frequency over the
course of a fixed time period
 Most common payment frequencies are
yearly,semi-annually,quaterly & monthly

3. Present Value (PV) of an Annuity
 Current value of a set of cash flows in the future
 Given a specified rate of return or discount rate
 Future cash flows are discounted at the discount
rate
 Higher the discount rate, the lower the present
value of annuity

4. Calculation of PV of an Annuity
Mathematically,
PV of an Annuity = C * [ 1- (1+i)-n ]/ i
where,
C = Cash flow per period
i = Interest rate
n = Number of payments

5. Future Value (FV) of an Annuity
 Value of a group of payments at a specified date in
future
 Measures how much a person would have in the future
given a specified rate of return or discount rate
 Future cash flow of annuity grow at the discount rate
 Higher the discount rate, higher is the FV of annuity

6. Calculation of FV of an Annuity
Mathematically,
FV of an Annuity = C* [ (1+i)n – 1 ]/ i
where,
C = Cash flows per period
i = Interest rate
n = Number of payments

7. Difference between Ordinary
Annuity & Annuity Due
Two types of Annuities:
1. Ordinary Annuities: Payments are required at
the end of each period.
Example: Bonds
2. Annuity Due: Payments are required at the
beginning of each period.
Example: Rent

8. Calculation of PV & FV of an
Annuity Due
Mathematically,
PV of an Annuity Due = C*[{ 1- (1+i)-n }/i] * (1+i)
FV of an Annuity Due = C*[{ (1+i)n – 1}/i] * (1+i)

9. Thank You