Question

A woman wants to retire at the age of 75 and receive $4,000 a month until the age of 100 where it will be penniless. She starts at the age of 25 with 20,000 and a 4% annual rate.

How much will she need to have in the policy at the age of 75 to be able to receive 4,000 a month for 25 years of retirement?

How much money will she need to add each month to meet this requirement?

Answer 1

Solution:

Solution:

First we need to compute present value of $4,000 monthly payments @ 4% at the time of retirement which can be computed as follows:

PV of future monthly income = Pmt.[ 1-(1+i)^-n ] / I

= $4,000*[1-(1+0.04/12)^-25*12 ] / (0.04/12)

= $757,809.93

Now, value generate by $20,000 initial investment at the end of retirement = $20,000*(1.04)⁵⁰

= $142,133.67

So, the remaining amount that needed to be generated = $757,809.93 - 142,133.67 = $615,676.26

This calculated value above is present value of the amount we will be accumulating till life expectancy. So, for getting $4,000 till life expectancy, we have to generate the above calculated amount at end of retirement (at 75th yr) by adding additional monthly to initial investment during working yrs. So, the amount needs to be added can be computed as follows:

Per month amount needs to be added = FV*i/[(1+i)ⁿ - 1 ]

= $615,676.26×(0.04/12) /[(1+0.04/12)^50*12

= $322.45 (rounded off) (Answer)

Note: If u have any additional rate of interest given in retirement period, please provide that rate in the comment section.