Question

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?

Answer #1

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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