Alonso’s income tax rate is 30%. Other than a small cash reserve, he holds all of his investment
assets in a tax-exempt account with a current value of USD 900,000. Contributions to this
account are made after tax. Withdrawals are entirely tax-free, without penalty. Alonso saves
USD 25,000 of his after-tax income every year, and plans to continue doing so until retirement.
His next contribution will be made in one year. As part of his normal expenses, Alonso annually
provides approximately USD 30,000 of support to local youth sporting leagues.
When Alonso retires in 15 years, he plans to purchase a 25-year annuity that pays USD 100,000
after tax annually. He will need USD 1,600,000 at retirement to fund the annuity. Alonso expects
the annual payout to be sufficient to meet all his needs on an inflation-adjusted basis. He does
not plan to leave any estate at his death.
Calculate the required annual return that would enable Alonso to purchase the retirement
annuity at age 55. Show your calculations ?
To calculate the required return needed to reach the target annuity future value, use the following
Number of years to retirement = 15
Annual savings = –25,000
Current portfolio value = –650,000 (900,000 – 250,000 trust
Target portfolio value = 1,600,000
Then solve for i:
i = 3.6467% or, rounded to 3.65%
I assume it’s one of those “trying to throw you off” type of extra info that is not needed for anything. It says “as part of his normal expenses”, and I would assume that if they explicitly say he is able to save 25k/yr, then his net income could not be negative 5k as that would be incongruent with a positive savings rate.
- You must be logged in to reply to this topic.