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# Archive for August, 2010

## Time Value of Money, Part-4

Posted by Prashant Shah on August 28, 2010

If Mr. A invests Rs.1000 per annum for next 10 years in a mutual fund which is earning 10% per annum. What amount of money will he receive after 10 years?

This is the question of annuity. Annuity means a series of cash flows at equal interval. Payments of EMI, receipt of salary are a few of the examples of annuity.

Annuity is of two types:

Annuity Due:  Where cash flow happens at the beginning of the period

Annuity End:  Where the cash flow happens at the end of the period

Let’s solve the above question considering Annuity End

We don’t get into formulae of the annuity and we will use a financial calculator

PMT = -1000

N = 10

i/y = 10

FV = ?

Calculation for Annuity Due:

PMT = -1000 (begin mode)

N = 10

i/y = 10

FV = ?

Alternatively you can multiply the annuity end answer with rate of interest to get the answer.

E.g.  15,937 × 1.1 = 17,531.

Annuity can also be in monthly/quarterly or semi-annual intervals. In that case we will alter N and i/y as we did in the Part-3 of the time value of money learning.

Mr. A has Rs.10,000 today and want to invest further Rs.1000 per year from today for next 10 years in a mutual fund earning 10% return. After 10 years he will get..

PV = -10000

PMT = -1000(begin mode)

N = 10

i/y = 10

FV = ?

Important: Here initial value and annuity both are taken negative because both are outflows.

## Time Value of Money, Part-3

Posted by Prashant Shah on August 27, 2010

How to use future value and present value concepts when compounding is not annual?

Let’s first of all understand the concept of simple interest and compound interest.

Simple Interest:

I invested Rs.100 for 3 years at simple interest of 10% per annum.

In this case interest = 100×10% = Rs.10

So Rs.10 will be paid over a period of 3 years and Rs.100 will be paid back as maturity value.

 Year Amt Rs. 1 10 2 10 3 10+100

Now instead, I invested Rs.100 for 3 years at compound interest of 10% per annum

There will be no intermittent cash inflows to me and whatever interest is accrued will be reinvested at 10% and I will get a lump sum at the end of 3 years.

 Year Amt Rs. at the end of year 1 100+10(interest @10%) = 110 2 110+11(interest @10%) = 121 3 121+12.1(interest @10%) = 133.1

Hence I will get Rs.133.1 at the end of 3 years. This is the concept of compound interest and it differs from simple interest. Practically majority of the investment products follow the concept of compound interest. Normally compounding can be made on monthly/quarterly/semi-annually/annual basis.

Semi-annual compounding:

Mr. A invested Rs.1000 in National Saving Certificate. Maturity is 6 years and rate of interest is 8% compounded semi-annually. What amount he will receive at maturity?

Solution:

PV = -1000

i/y = 8/2 = 4 (as compounding is semi-annual)

N = 6×2 = 12 (as compounding is semi-annual)

FV = ?

Quarterly compounding:

Mr. A invested Rs.1000 in bank fixed deposit. Maturity is 5 years and rate of interest is 8% compounded quarterly. What amount he will receive at maturity?

PV = -1000

i/y = 8/4 = 2 (as compounding is quarterly)

N = 5×4 = 20 (as compounding is quarterly)

FV = ?

Monthly Compounding:

Mr. A invested Rs.1000 in company fixed deposit. Maturity is 5 years and rate of interest is 12% compounded monthly. What amount he will receive at maturity?

PV = -1000

i/y = 12/12 = 1 (as compounding is monthly)

N = 5×12 = 60 (as compounding is monthly)

FV = ?