Question

you just turned 25 years and want to retire when you turn 65. you plan to put $3,500 every year into retirement account from which youncan withdraw money after retirement without having to pay any taxes. you expect to earn a return of 7% on your investments every year. how much money you can expect to have at age 65 if you make your annual deposit now and your last one on the day you turn64?

Answer 1

here last contribution made is at end of year 64 , hence we first need to find balance at end of year 64. Since first deposit is made now , formula of future value of annuity will be used

Annuity = 3500 $

r = rate of interest = 7%

n = no of years = 65 ( Note sinse the first payment is made now , total no of payments will be 65)

FV(annuity due)= A[(1+r)^n - 1 / r]

= 3500[(1+7%)^65 - 1 / 7%]

= 3500[(1+0.07)^65 - 1 /0.07]

= 3500[(1.07)^65 - 1 /0.07]

= 3500[ 81.2729 - 1 / 0.07]

= 3500[ 80.2729 / 0.07]

= 3500 x 1146.7552

= 4013643.06 $

Now formula of future value shall be used to find balance at end of year 65

FV = PV(1+r)^n

n = 1

PV = 4013643.06

r = 7%

FV = 4013643.06(1+7%)^1

= 4013643.06(1.07)

= 4294598.08 $

Thus at end of year 65 , account balance will be 4294598.08 $