Question

Suppose that you are 23 years old, and making retirement plans. You are starting to contribute $550 per month to your retirement account at the beginning of each month. You intend to do so until the age of sixty three and then stop the contributions. You will retire at age 67. You receive a 6.5% APR compounded monthly on your account. Starting at age 67, what could you withdraw in terms of a monthly annuity until age 99 assuming you can get the same 6.5% APR on your money?

Group of answer choices

$10200-$10400                                                          

$9600-$9800

$10000-$10200

$9800-$10000

> $10400

Answer 1

Periodic monthly contribution at the beginning of each month = $550

Contribution is started at age 23 and contributed until age 63 which means contribution made for 30 years. And thereafter interest is accrued on accumulated amount till age 67,i.e, only interest is accrued further for 4 years.

Calculating the Accumulated amount at age 67:-

Where, C= Periodic deposits = $550

r = Periodic Interest rate = 6.5%/12 = 0.541666%

n= no of periods for which contribution is made= 40 years*12 = 480

m = no of periods for which interest accrued = 4 years*12 = 48

Future Value at age 67 = $1,636,602.28

- Now at age 67, monthly annuity is withdrawal from above accumulate fund account till age 99. Calculating the Periodic annuity withdrawal:-

Where, C= Periodic Payments

r = Periodic Interest rate = 6.5%/12 = 0.541666%

n= no of periods = (99 years - 67 years)*12 = 384

Future Value = $1636,602.28

C = $10,138.68

So, you would withdraw in terms of monthly annuity of $10,138.68

Option 3. $10000-$10200

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