draw a discrete cash flow diagram for the situation described 25. A 401k (and si

Question

draw a discrete cash flow diagram for the situation described

25. A 401k (and similar plans) is an investment vehicle available to most individuals to save for retirement. The benefit is that the investment is made before taxes (by payroll deduction), and interest is not taxed until the money is withdrawn. In theory, most retirees are in a lower tax bracket than when they worked. Under current laws (2016), the maximum annual contribution to all such plans in 2016 is $18,000 until age 50 and $24,000 thereafter, including the year one turns 50. Suppose that the maximum contribution is made every year for 40 years, beginning at age 25 until age 65. (Note: Employers may match this contribution, but this is not considered here.) 1. What is the future value of this retirement fund after 40 years, assuming an effective annual interest rate of 9%? 2. What effective annual interest rate is required for the future value of this investment to be $2 million after 40 years?

Explanation / Answer

1.

Investment start age - 25

Final investment - 65

Amount invested till age of 49 = 18000

Amount invested 50 years>

Rate = 9%

Now, amount which is invested when age was 25 will get compounded 40 time till the age of 65

So 18000 * (1.09)^40 = C25

Similarly when age 26, C26 = 18000 * (1.09)^39 and so on

Amount invested at the age of 49 = C49 = 18000 * (1.09)^16

So total cash flow till the age of 49 = 18000 [ (1.09)^40 + (1.09)^39 + (1.09)^38...............+(1.09)^16]

total cash flow till the age of 49 = 6,053,192.40

Similarly,

amount deposited at the age of 50 = 24000

Amount = 24000 * (1.09)^15 and so on

So total amount = 24000 * [(1.09)^15 + (1.09)^14 +(1.09)^13..............+(1.09)^0)]

So total amount = 792,081.57

So total amount in 40 years = 6,053,192.40 + 792,081.57 = 6,845,273.96

2.

To find effective rate so that total amount will be 2,000,000 is by hit and trial. We have to use above mentioned cash flows and try and see at what rate the total value is coming to be 2,000,000

The rate at which we will achieve 2,000,000 = 4.158%

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