Question

# Javier hopes to live 50 more years from today and plans to retire in 30 years...

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:

• Starting today, Javier will make monthly contributions at the beginning of each month, which will grow at 0.15% effective monthly. The first contribution Javier will make to the savings fund is for an amount of \$1,000.
• The interest rates will be:
• 1% effective monthly for the next 30 years (from today)
• Subsequently, 0.75% effective monthly.

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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