Question

The first year after you retire you want to be able to withdraw $100,000 from your savings account. Every year after that you want to increase your withdrawals by 2%. You expect that the account will earn 6% annual interest. How much money must you have in your savings account when you retire to make sure that your money lasts for 25 years

Answer 1

Total amount of money to be had in savings is $1,544,352.63

Step-by-step explanation:

First withdrawal is $100,000 and is increases by 2% every year till 25 years.

The amount required in savings account can be calculated by knowing the present value of growing annuity.

Annuity =
`(p /(r-g) *[ 1 -(1+g / 1+r)^n]`

given, p = $100,000

r = 6% = 0.06

g=2% = 0.02.

n = number of periods = 25.

= (100,000 ÷ (0.06 - 0.02)) × [ 1 - (1.02 ÷
`1.06)^{25` ]

= $2,500,000 × [1 - 0.382258949]

= $2,500,000 × 0.61774105

= $1,544,352.63