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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