Javier hopes to live 50 more years from today and plans to retire in 30 years (from today). During his retirement he would like to receive, at the end of each month, a constant retirement income. Javier’s savings plan during his working life is as follows:
How much will Javier’s monthly income be during his retirement?
First Contribution (P)= 1000
Growth in Contribution (g)= 0.15%
Number of months in 30 years (n)= 30*12= 360
Interest rate per month for deposit (I)= 1%
As deposit is made at Beginning of month, so it is growing Annuity due. Future value of growing Annuity due Formula will become applicable.
Future value of growing annuity due=first Annuity*(1+I)/(i-g)*(((1+i)^n)-((1+g)^n))
=1000*(1+1%)/(1%-0.15%)*(((1+1%)^360)-((1+0.15%)^360))
=4067843.753
This is value at end for future Annuity wirhdrawal.
So present value at year 30= 4067843.753
Number of withdrawal in 20 years (n)= 20*12= 240
Interest rate per month (I)= 0.75%
Monthly Income or wirhdrawal shall be calculated by Annuity Formula.
Annuity Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)
4067843.753*0.75%*((1+0.75%)^240)/(((1+0.75%)^240)-1)
=36599.44609
So Monthly Income in retirement would be $36599.45
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