Annuity

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

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

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

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

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

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

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)

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