Solution of Problems in Annuities of Organisational Finance

Problem

This is a humble request from you to find some useful tips on Annuity, Sir, I'm a student of Masters in Professional Accounting from Sydney University, Australia, I am facing problems in Annuity (both Future and Present).

I have been learning many things from your blog and I have also registered with ur email. So, Kindly email me regarding Annuities of Organisational Finance, one of the subjects of Masters.

Solution

Dear student,

For solving annuities problems of your organisational finance subject, you have to understand the meaning of annuity. After this, you can go deep in it.

Q:- 1.  What is Annuity?

Ans. : When you purchased an asset on credit, you have to pay the amount purchased asset in installments. That installment is called Annuity.

For Example

Suppose, you have to go to Sydney University, Australia from your house which is about 60 km. far from your own house where you are living. Now, you go to your local financial institute and finance your car. You can fix that you have to repay the amount of car with in 12 installments. These installments will be annuities.

More deep explanation of Annuity:

 Above was the simple definition and example of annuity but we can explain more deeply it. Above is only that type of annuity which is fixed for its future time . For example , if we purchase a car and if agreement fixes the 10 installment of payment , then these annuities will be called annuity certain. We also fix Perpetuity or perpetual annuity. It is that type of annuity which is payable all the time . There is no end of these annuities . For example , if a person has taken life insurance policy , then if he pays its premium up to his life , these these annuities will be called perpetuity or perpetual annuity.If  Any annuity whose payment is closed after some time , then these annuity is called forborne annuity .

I think you understand the meaning of Annuity and its different types. Now, I am taking second step for calculation of annuity. You have to understand the steps to calculate the annuity.

Q: 2 How to Calculate the Annuities?

Ans.  In organisational finance, we need to calculate different annuities different Techniques of Mathematics Finance.

First Technique of Calculating Annuity

If you have to buy any car , TV , or any other product , then this formula can used for calculating value of annuity . In many questions , you will see that buyer will pay some amount when he buys product , so deduct it from principle amount .


For example :

A man purchases a refrigerator by making a cash payment of Rs. 5000. In addition he has to pay Rs. 1000 at the end of each six month for 4 years. If money is worth 10% compounded semi-annually find cash- price for refrigerator.

Solution

This problem, we can only solve, if we know first technique to calculate the annuity.

Cash price of refrigerator - cash payment =

Value of Annuity X [ 1- (1+r/100) and its power minus t / r/100 ]

Or

Cash price of refrigerator =

cash payment + Value of Annuity X [ 1- (1+r/100) and its power minus t / r/100 ]

cash price of refrigerator = 5000 + 1000{ 1- (1+5/100) power - 8 / 5/100 }

Cash price of refrigerator = Rs. 11466


Second Technique of Calculating Annuity


If you have created any fund to buy new fixed asset or repay the amount of long term loan or debentures,  then second formula is more simple than first


For example

A person sets up a sinking fund in order to collect RS. 50, 00, 000 after 19 years for his child education in Sydney University, Australia. How much amount should he set aside into an account paying 5% p.a. Compound half yearly.

Solution :

Total target of person to save = Rs. 50,00,000 in 10 years because he will send his child to Sydney university, Australia for higher education and I think Rs. 50,00,000 will be needed to go to Australia for study  in 2020.

rate = 5% p.a. or 5/2 % half yearly

time or t = 10 x 2 =20


Total saving =


Amount or annuity or installment for sinking fund { ( 1+r/100) power number of time - 1 / r/100}

50, 00, 000 =  Annuity  { ( 1+ 5/200) power 20 -1/ 5/100}

Amount of Annuity = 50,00,000 X 1000 / 4 X 675 = Rs. 185100.80

So, that person have save 185100.80 set aside every six month for his child education in Sydney university, Australia.