Question

3. The Rule of 72 is a very useful approximation for understanding exponential growth. The Rule states that (72 / the interest rate) = doubling time. For example, if the interest rate is 10% and you invest $10 today, in 7.2 years you will have $20. (72/10 = 7.2, the doubling time) My sister, a financial planner, would suggest that you save today for peace of mind. So today, let's put $1,000 in a mutual fund that rather consistently yields 12%. You plan to retire at age 62. How much will the investment be worth at retirement, if you are now 50 years old? How much, if you are now 38 years old? How much, if you are now 20 years old? 120X20- Now you can see why financial planners stress that it is important to start saving early in your life, even if you can only save a little each month. Of course, what we are most concerned with in this class is people and their relationship with the physical world. So instead of being concerned about 1,000 dollars, we concern ourselves with the standard of living of the now 6,000,000,000* of us who are your relatives. (On a Tuesday in October of 1999, global human population surpassed six billion nice folks!) Write a paragraph (with a topic sentence) about exponential human population growth and its implications to the future.

Answer 1

Based on the Rule 72,

The states that (72/the interest rate)=Double Time

Let us compute the double time period for the given situation where $1,000 are invested @ 12% for 62 Years.

Double time = 72/Interest rate

=72/12

=6 years

That means when we invest $10 it double in 6 years

i) Investment worth at retairment(62 years) if you are now 50 years old.

Computation of Remaining years = Retairment age - Present age

Remaining Years = 62-50=12 Years

As we computed the double time as per the Rule 72 is 6 years

The years left are twice the double time

Hence, the amount which is going to be realized at the time of Retairment age is =

The amount is going to be double twice in the 12 years

i.e, 4 times the amount you invested = (2*2)*$1,000 = $4,000.

ii) Investment worth at retairment(62 years) if you are now 38 years old.

Computation of Remaining years = Retairment age - Present age

Remaining Years = 62-38=24 Years

As we computed the double time as per the Rule 72 is 6 years

The years left are four times the double time

Hence, the amount which is going to be realized at the time of Retairment age is =

The amount is going to be double four times in the 24 years

i.e, 4 times the amount you invested = (4*2)*$1,000 = $8,000.

iii) Investment worth at retairment(62 years) if you are now 20 years old.

Computation of Remaining years = Retairment age - Present age

Remaining Years = 62-20=42 Years

As we computed the double time as per the Rule 72 is 6 years

The years left are seven times the double time

Hence, the amount which is going to be realized at the time of Retairment age is =

The amount is going to be double seven times in the 42 years

i.e, 4 times the amount you invested = (7*2)*$1,000 = $14,000.