Question

Suppose that you are 21 years old, and making retirement plans. You are starting to contribute $800 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 5% APR compounded monthly on your account. How much will you have if you allow interest to accrue to age 67? (K means 1,000's)

Group of answer choices >

> $1690K

$1680K - $1690K                                                        

< $1660K

$1660K -$1670K

$1670K -$1680K

Answer 1

Periodic monthly contribution at the beginning of each month = $800

Contribution is started at age 21 and contributed until age 63 which means contribution made for 32 years. And thereafter interest is accrued on accumulated amount till age 67,i.e, only interest is accrued for 4 years.

Calculating the Accumulated amount at age 67:-

Where, C= Periodic deposits = $800

r = Periodic Interest rate = 5%/12 = 0.41666%

n= no of periods for which contribution is made= 42 years*12 = 504

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

Future Value = $1678,424.06

So, Future Value at age 67 is $1678,424.06 or $1678K

Option 5. $1670K -$1680K

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