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? Please enter your answer rounded to the nearest dollar, with no dollar signs or formatting included. For example, enter the answer $40,576.34 as 40576

Solutions

Expert Solution

Contribution per anum = Annual Salary * 12%

= $ 6000

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

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

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

jeff jeffy answered 1 year ago

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