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**MBA Finance study material**. Show all posts## Thursday, June 5, 2014

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Thursday, June 5, 2014
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## growing annuity example future value formula excel

Question:You are considering
whether your savings will be enough to meet your retirement needs.You saved
100,000 last year and you expect your annual savings to increase by 8 percent
per year for the next 20 years.if your savings can be invested at 9 percent,how
much you would have at the end of twentieth year?

Solution:In 0th year you will have 100000 with you.Given this
amount is growing at 8 percent per year.So at the end of 1st year your amount will be 100000*(1.08).In second
year it will 100000*(1.08)^2

At the end of 20th year this amount will be 100000*(1.08)^20

Given that we are
investing these amounts at 9 percent.

So the future value at
the end of 20th year will be

Let 100000 be denoted
by 1 lakh

Therefore future value

=1.09^20
+1.09^19*1.08+1.09^18*1.08^2+........................+ 1.08^19*1.09+ 1.08^20

This is a Geometric
Progession with first term as 1.09^20 and G.R as 1.08/1.09

Therefore using the
formula for a G.P with G.R<1

Sn=A*(1-GR^n)/(1-GR)

Where A is the first
term which is =1.09

GR is Geometric ratio
which is =1.08/1.09

n=21 as we have 21
terms in the sum equation

Therefore
Sum=1.09^20*(1-(1.08/1.09)^21)/(1-(1.08/1.09))

=107.5 Lakh

Please do comment below if you got any doubt.

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## present value of money questions with answers present value formula

Present Value Formula

P.V=F.V/(1+r)^n

What is the present
value if the future value is 100000 and
n=10,Assume r=10%

P.V=F.V/(1+r)^n

=100000 /(1.1)^10

=3855

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## future value of money questions with answers future value of money formula

Future value formula=P*(1+r)^n

Question:A invests
Rs.10000 when he started working at the age of 25.He retires at the age of
55.What will be the future value of the money at the time he retires. Assume
rate of interest=10%.

Soln:P=10000

r=.1

n=30

F.V=P*(1+r)^n

F.V=10000*(1+.1)^30

=Rs.
174494

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