Question

In example 6.2.4, and employee is able to contribute $123.25 to a 100% employer-matched 401(k), which is invested at an average APR of 6.3% compounded monthly. After 11 years, the employee retires.

What is the size of the monthly contribution after the
employer match is accounted for? PMT =

What was the future value of the account after 11 years?

In parts b and c, the account grows for 14 more years without any additional contributions or withdrawals from the employee.

What future value did the account reach after the extra 14 years?

How much total interest was earned over the course of the 25 year investment?

Enter your answer without a dollar sigror comma. For example, 9703.52

Answer 1

[AI-generated answer — Bot GPT 3.5]

a) PMT = $123.25 + $123.25 = $246.50

b) The future value of the account after 11 years can be calculated using the formula for compound interest: FV = PV(1 + r/n)^(nt), where PV is the initial investment, r is the annual interest rate (6.3% = 0.063), n is the number of compounding periods per year (12 for monthly compounding), and t is the number of years. In this case, PV = $246.50, r = 0.063/12 = 0.00525, n = 12, and t = 11.

FV = $246.50(1 + 0.00525/12)^(12*11)
FV = $246.50(1 + 0.0004375)^132
FV = $246.50(1.0004375)^132
FV ≈ $488.90

c) To find the future value of the account after the extra 14 years, we use the same formula but with t = 14.

FV = $488.90(1 + 0.00525/12)^(12*14)
FV = $488.90(1 + 0.0004375)^168
FV = $488.90(1.0004375)^168
FV ≈ $988.24

d) The total interest earned over the course of the 25-year investment can be found by subtracting the total contributions from the total future value of the account:

Total interest = FV - (PMT*12*25)
Total interest = $988.24 - ($246.50*12*25)
Total interest = $988.24 - $73950
Total interest ≈ $248.24