# time_value_of_money

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Category: Education

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## Presentation Transcript

### Slide 1:

Future Value Present Value Present Value of Annuity Future Value of Annuity TIME VALUE OF MONEY

### Slide 2:

Where: FV: Denotes future value PV: Denotes Present Value R: Denotes the annual rate of interest M : Denotes the period of compounding N : Denotes the number of years

### Slide 3:

Calculate the future value of Rs.1000 invested @ 4% for 4 years (Annual Compounding). What if the rate is compounded semi-annually?

Answer Annual Compounding 1169.86 Semi-annual compounding 1171.66

### Slide 5:

Here Is termed as future value interest factor. The value of this can be directly taken from the following table, by looking at R/m rate against n*m period

### Slide 6:

Future Value Interest Factor

### Slide 7:

Where: FV: Denotes future value PV: Denotes Present Value R: Denotes the annual rate of interest M : Denotes the period of compounding N : Denotes the number of years

### Slide 8:

Calculate the present value of Rs.1000 payable at the end of 4 years @ of 4%.

### Slide 10:

Here the fraction Is termed as present value interest factor. The value of this can be directly taken from the following table, by looking at R/m rate against n*m period

### Slide 11:

Present Value Interest Factor

### Slide 12:

Present Value of Annuity Annuity means equal payments made annually. The objective is to compute the present value of equal annual payments. Assuming an amount A is paid at the end of every year for 3 years. So the present value of all the three payments right now is:

### Slide 13:

Rs.8000 is deposited by Mr. Ram every year for 3 years. The deposit is made at the end of each year. The bank offers interest of 3% compounded annually. What is the present value of the annuity?

### Slide 15:

Here the expression: Is termed as present value annuity factor and can be directly seen from the table for R/m rate for a period of 3 years.

### Slide 16:

Present Value Annuity Factor

### Slide 17:

Future Value of Annuity Annuity means equal payments made annually. The objective is to compute the future value of equal annual payments. Assuming an amount A is paid at the end of every year for 3 years. So the present value of all the three payments at the end of three years is:

### Slide 18:

Rs. 8000 is deposited by Mr. Ram every year for 3 years. The deposit is made at the end of each year. What is the future value of the annuity at the end of 3 years? (Assume a rate of 3% annually compounding)

### Slide 20:

Here the expression Is termed as future value annuity factor. The value of this can directly be seen from future value annuity table by looking for R/m rate along with 3 years time period.

### Slide 21:

Future Value Annuity Factor

### Slide 22:

Calculate the present value of an annuity of Rs.8000 starting at the end of 3 years and lasting till the end of 7th year. Assume a discount rate of 10%. 25050.93

### Slide 23:

An investment company offers to pay Rs.25,959 at the end of 10 years to investors who deposit Rs.1000 annually. What is the implied rate of return?

20%

### Slide 25:

At the time of his retirement Mr. Swamy is given a choice between two alternatives: Annual pension of Rs.20,000 as long as he lives. A lump sum payment of Rs.1,50,000. If he expects to live for 15 years and the rate is 15%, then which alternative should he select?

Answer Present value of annuity is 1,16,940 So Mr. Swamy should choose option (b)

### Slide 27:

Recently acquired your MBA in finance you are very confident about your investment skills. Your father is willing to give you your share of family wealth. He however gives you an option of choosing between Rs. 10 lakh right now or 2 lakh each year for next 6 years. Assuming you are confident of earning 15% per year on your investment, which offer of his would you accept? What if you are confident of earning 25%?

### Slide 28:

Payment of a 9 year annuity of Rs. 10,000 will begin at the end of 7 years. What is the present value of the annuity? Assume a rate of 12%.

### Slide 30:

Assume that you are given a choice between incurring an immediate outlay of Rs.10,000 and having to pay Rs.2310 a year for 5 years (first payment due one year from now); the discount rate is 11%. What would be your choice? Will your answer change if Rs2310 is paid in the beginning of each year for 5 years?

Answer (a) Present Value of annuity is 8537.76 (b) Present value of annuity is 9475.62

### Slide 32:

You plan to buy a flat for Rs.200, 000 by making Rs. 40,000 down payment. A house financing company offers you a 12 year mortgage requiring end of the year payments of Rs.28,593. The company also wants you to pay Rs. 5000 as the loan processing fee which they will deduct from the amount of loan given to you. What is the rate of interest on loan?

### Question :

Question If a person deposits Rs.1000 on an account that pays him 10% for the first five years and 13% for the following eight years, what is the annual compound rate of interest for the 13 year period

11.83%

### EFFECTIVE RATE :

EFFECTIVE RATE Effective rate of interest is that annual rate which produces the same effect as that produced by nominal rate when compounded under less than annual time periods.

### Slide 37:

If 9% p.a. nominal rate is compounded semi-annually then what is the effective rate of interest?

9.2025%

### Question :

Question If the nominal rate of interest is 12% per annum calculate the effective rate of interest when a sum is compounded (a) annually (b) semi-annually (c ) quarterly

### Slide 40:

12% 12.36% 12.5509%

### Question :

Question If the nominal rate of interest compounded quarterly results in effective rate of 18%, then calculate the nominal rate of interest.

16.8987%

### Question :

Question City Finance Ltd. has various deposit schemes which offer the same effective rate of interest as 10% per annum compounded half yearly. If you save Rs.100 at the beginning of every month with CFL in a monthly recurring deposit scheme which has a maturity of three years, then what will be the maturity value at the end of three years?

Rs.4165.38

### Rule of 72 :

Rule of 72 The period within which the amount will be doubled is obtained by dividing 72 by the rate of interest.

### Question :

Question As per the rule of 72 in how many years will the amount deposited today at an interest rate of 16% double?

4.5YEARS

### Slide 48:

If you deposit Rs.10,000 today at 12% rate of interest, in how many years does this amount grow to Rs.80,000 (Rule of 72)

### Rule of 69 :

Rule of 69 Doubling period = 0.35+69/ Interest rate What is the rate of interest when the doubling period is 7 years 4 months?

9.88%

### Slide 51:

If the long term rate of interest offered by a bank is 6.19% per annum. What is the doubling period under rule of 69?

11.497 yrs

### Question :

Question Ms. Kusum has retired recently. She received Rs.5 lakh as her retirement benefits, which she had invested in a bank at 15% rate of interest. If she expects to live independently for another 15 years, how much money she can withdraw at the end of every year so as to leave a nil balance in her account at the end of maturity?

### Slide 54:

A loan of Rs.500,000 is to be paid in 10 equal annual installments. If the loan carries a rate of interest of 12% p.a., what is the equated monthly installment?

### SINKING FUND :

SINKING FUND Sinking fund is a fund which is created out of fixed payments each period to accumulate to a future sum after a specified period.

PERPETUITY