## Time Value of Money, Part-5

Posted by Prashant Shah on August 30, 2010

If you want 1crore rupees after 35 year, what amount of money will you have to invest from today? (Assume rate of return as 12% p.a.)

This is the question of future value of annuity where we will have to find payments

FV = 10000000

N = 35

i/y = 12

PMT =? (Begin mode)

**Answer: 20684**

Let say you want to invest on monthly basis for the same amount, then

FV = 10000000

N = 35×12 = 420

i/y = 12/12 = 1

PMT =? (Begin mode)

**Answer: 1540**

Now another topic, let say you have taken a loan @ 12% for 10 years of Rs.10 lakh, what will be the EMI?

This is the question of present value of annuity and we are finding payments here.

PV = 1000000 (Inflow hence positive)

N = 10×12 = 120

i/y = 12/12 =1

PMT = ?

**Answer: 14347**.

**Remember:** EMIs are always paid at the end of the period, hence no need to assume begin mode.

Present value of annuity is useful to find current value of all the future payments.

Mr. A asks you to lend some money to him. He agrees to pay you Rs.1000 per month over a period of next 5 years. Prevailing rate of interest is 12% per annum. What amount of money should you lend him today?

PMT = 1000

N = 5×12 = 60

i/y = 12/12 = 1

PV = ?

**Answer: 44955.**

## Darshan said

Sir,

In the 1st Question above regarding monthly invest to be made the answer should be 1814.60 plz let me know if I m correct.

## Prashant Shah said

Dear Darshan,

1540 is the correct answer.

Request you to show your method.

Prashant.

## Darshan said

Sir,

If we Solve this by Calculator,

Set: Begin, n=35*12, I = 12, FV = 10000000 , pmt = (Solve) -1814.60 , P/Y =12, C/Y = 1

## vinay said

Darshan

the problem you mentioned is an old one, ie it is solved according to old method of calculation of monthly rate of compounding- dividing the intrerest rate by 12 simply. But in your method what you have taken is effective rate of compounding- ie 11.386. This is the method prescribed by FPSB now.

In the solution if you replace i= 12/12 by 11.386/12, you get your answer. So treatment of rate of interest for the month is the cause for difference in the answers.

## udaycfpudaycfp said

Let say you want to invest on monthly basis for the same amount, then

FV = 10000000

N = 35×12 = 420

i/y = 12/12 = 1

PMT =? (Begin mode)

Answer: 1540

i got another ans= -1814.60

set-b N-35*12 I-12% PV -0 PMT=? [SOLVE = – 1814.60] FV=10000000 P/Y=12 C/Y =1

if the interest rate is comp. monthly then ans = 1540.

set-b N-35*12 I-12% PV -0 PMT=? [SOLVE = – 1814.60] FV=10000000 P/Y=12 C/Y =12

where say question interest is comp. monthly.

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If you want 1crore rupees after 35 year, what amount of money will you have to invest from today? (Assume rate of return as 12% p.a.)

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