Question

What are examples of times you would need to solve for the cash flow in an annuity?

Answer 1

Calculation of  annuity of cash flows related to times with example are given below.

Definiton

An annuity is a cash flow, in terms of income or outgoings, involving the same sum in each period. An annuity is the payment or receipt of equal cash flows per period for a specified amount of time. For example, when an organisation set aside a fixed sum each year to meet a future liabilities,by applying  annuity method. The time period between two successive payments is called ‘payment period’.

The word ‘annuity’ is broader term, which includes payments which can be annual, semiannual, quarterly ,Annuity does not necessarily mean payment taken to be one year

Examples related to times in Cash Flow annuity.

Lets us take a example (1)

X Ltd. intend to invest Rs.15,000 per annum at the end of years 5,6,7 and 8 at an annual interest rate of 12%. Find out the present value of the deferred annuity payments.

Solution:

Example (2)

X Ltd. had taken a freehold land for an annual rent of Rs.1,800. Find out the present value of Leasehold Property which is enjoyable in perpetuity if the interest rate is 10% p.a.

Solution

V = P/i = 1800/0.10 = 18,000

Where P = Annual Rent and i = Interest rate.

Example (3)

Suppose, Mr. Y is depositing Rs.8000 annually for 4 years, in a Nationalised Bank account at an interest of 5% p.a. Find the present value of annuity cash flow.

Solution

P = Rs. 8,000 i = 0.05 n = 4

Let:

x = (1.05) ^-4

Log x = -4 log 1.05 = -4 x 0.0212 = -0.0848

= -1 + 1 – 0.0848 = 1̅.9152

x = antilog (1̅.9152) = 0.8226

V = 1,60,000 x (1 -0.8226) = 1,60,000 x .1774 = Rs.28,384