Question

John and Mary are both 26 and newly married. They come to you for a financial plan. They have saved $10,000 in their retirement accounts and just purchased a $150,000 house by paying a $30,000 down payment. They would like to retire in their mid to late sixties. John and Mary believe they will need to accumulate $1,500,000 in their retirement accounts in order to retire comfortably. You have recommended an investment strategy earning 10% on an annualized basis for John and Mary. They ask you to tell them how much they will need to save at the end of each quarter in order to retire at age 67 with $1,500,000.

Answer 1

Given,

Current age= 26 and retirement age= 67

Therefore, period of savings= 41 years.

Amount to be saved at the end of each quarter= F/(1+r)^n*r/(1-(1+r)^-n)

Where

F= Future value required

r= interest rate per quarter= 10%/4 = 2.5%

n= number of payments= 41*4= 164

Amount required in retirement account= $1,500,000 and Current savings= $10,000

Hence F= 1,500,000-10,000*(1+2.5%)^(41*4) = 1500000-573738.41= $926,261.59

Plugging the values,

Amount to be saved at the end of each quarter= 926261.59/(1+0.025)^164*0.025/(1-(1+0.025)^-164)

= 403.607976/ 0.98257045   = $410.77