Question

Assume that Annie makes $50,000 a year for the next 30 years (she works for 30...

Assume that Annie makes $50,000 a year for the next 30 years (she works for 30 years total). During her entire career, she contributes 8% of her salary to her 401K, and her employer matches 4% of her salary (meaning her total contribution to her 401K is 12% of her salary annually). What is the FV (value in 30 years, or value upon her retirement) of all of Annie’s annual 401K contributions over the 30-year period assuming she earns 9% per year on her 401K investment portfolio?

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Answer #1

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

EMployee Share = 8%

Employed Share = 4%

Total share towards 401(K) Plan = 12%

12% of Salary = 12% of $ 50000

= $ 6000

Particulars Amount
Cash Flow $      6,000.00
Int Rate 9.000%
Periods 30

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 6000 * [ [ ( 1 + 0.09 ) ^ 30 ] - 1 ] / 0.09
= $ 6000 * [ [ ( 1.09 ) ^ 30 ] - 1 ] / 0.09
= $ 6000 * [ [13.2677] - 1 ] / 0.09
= $ 6000 * [12.2677] /0.09
= $ 817845.23

Answer is 817845

Pls comemnt, if any further assistance is required.

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