ABM- Caiib Book- Time Value of Money Solution

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1.  I am 50 years old,retire at the age of 60 and expect to live 10 years more. If I want to spend Rs. 10000 per month, How much should I save by the age of 60 years to support this Plan. Assume Interest rate of 8 percent.What is the required saving if the interest rate is only 5 percent?

Solutions:
Let us assume that Mr. Subhash (Assumption ) spend the Rs.10000 at the end of month during his retirement life.At the time retirement should hold money in hand to spend Rs.10000 every month, We need to calculate present of value of cash flow

At the Rate of 8% per year , we will calculate Present value of Annuity Due: Apply formula , I use excel for calculation. You can use Annuity table or scientific calculator

Ans. Rs. 829709.57

At the Rate of 5% per year, - Rs. 9,46,741.89

2. How long will it take to grow from Rs.500 to Rs. 2000?

a] If interest Rate is 4%, Future value of Rs.500
      FV= CF(1+R)ⁿ

3. What is the effective Interest Rate?

A) 12% Compounded Monthly 

B)8% Compounded every months

 

4. I invest Rs.5000 today to purchase an item to sell it at Rs.10000 after 8 years. If the interest rate is 5% p.a. is the good deal? What is the interest rate is 12% p.a.

Ans: There is three scenario , first Rs. 5000 is getting double after 8 years.

What is the Future value of Rs.5000 @ 5%
FV= CF(1+R)ⁿ
FV= 5000(1+.05)⁸
FV= 7387.277

What is the Future value of Rs.5000 @ 12%

FV= CF(1+R)ⁿ
FV= 5000(1+.12)⁸
FV=12379.8158814741

Clearly Showing that third option of Rate of interest 12% is good.

5. How much should be deposited at the beginning of each year for 10 years,in order to provide a sum of Rupees Five lakh at the end of 10 years?

 Solution: Lets Assume that Interest Rate is 10%, then calculation of Future value of Annuity Due

 If interest is not taken, deposit Rs. 50000 per month.

6. Ravi Receives Rs. 10 Lakh from provident fund. He deposits this amount in his bank and earns 10% interest. If he withdraw 2 Lakh ever years, what will be the amount left in his bank account at the end of 5 years? 

Solutions: This problem is solved by cash flow, 

click on Image to enlarge

7. Ram is saving to buy a car after 5 years. The car costs Rs.6 Lakh and he earns 8 percent per year on saving. He wants to save equal amount each year. 

a) How much does he need to keep aside at the end of 1 to 5 years?

Apply the future value of Ordinary Annuity for cash Flow

B) Suppose that Interest rate decrease from year 3, He still wants to go ahead with purchase of the  car at the end of year 5. By How much should he increase his savings?

For First Two Year

Payment Flow: 8165
Interest Rate: 8%

Fund after two year : Rs.211744

From year 3, Interest rate decreses by 2%
 Hence Intt. Rate for next three year = 3 %

Required Amount for car in next three year

Amount should be increased with Rs.1705.

C) If he follows earlier pattern of Savings, when he will be able to buy car?

He can buy after six years and 5 months.