You and your wife are making plans for retirement. You plan on living 30 years after you retire and would like to have $80,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 15% annually.

What amount do you need in your retirement account the day you retire?

The amount needed in retirement account on the day of retiring is $525,278.37

Explanation:

Data provided in the question:

Time, n = 30 years

Annual payment = $80,000

Interest rate = 15% = 0.15

Now,

The amount needed in retirement account

= Annual payment * [ {1 - (1 + r) ⁻ⁿ } : r ]

or

= $80,000 * [ {1 - (1 + 0.15) ⁻³⁰ } : 0.15 ]

or

= $80,000 * 6.566

or

= $525,278.37

Hence,

The amount needed in retirement account on the day of retiring is $525,278.37