Question

If Derek plans to deposit $12,231.00 into his retirement account on each birthday beginning with his 26th and the account earns 6.00%, how long will it take him to accumulate $3,670,397.00? Submit Answer format: Number: Round to: 2 decimal places Derek decides that he needs $106,459.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $106459.0 on each birthday from his 66th to his 90.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 8.00% Submit Answer format: Currency Round to 2 decimal places

Answer 1

1). Future Value of Annuity Due = (1 + r) * Annual Deposit * [{(1 + r)ⁿ - 1} / r]

$3,670,397 = (1 + 0.06) * $12,231 * [{(1 + 0.06)ⁿ - 1} / 0.06]

$3,670,397 = $216,081 * [(1.06)ⁿ - 1]

$3,670,397 / $216,081 = (1.06)ⁿ - 1

(1.06)ⁿ = 16.9862 + 1

n[log(1.06)] = log(17.9862)

n[0.0583] = 2.8896

n = 49.59

So, it will take 49.59 years to reach the goal.

2). Amount needed in Retirement Account = Annual Withdrawals * [{1 - (1 + r)^-n} / r]

= $106,459 * [{1 - (1 + 0.08)^-25} / 0.08]

= $106,459 * [0.8540 / 0.08]

= $106,459 * 10.6748

= $1,136,426