Question

Assume that cigarettes cost $7 per pack and consider a 21 year old college student smoker who smokes 15 packs of cigarettes per month. If the student quits smoking and each month invests the amount she would have spent on cigarettes in a savings plan that averages a 4% annual return, how much will she have saved by the time she is 65?

Answer 1

Answer:

The answer is $57657.6

Step-by-step explanation:

First, you must determine the amount of money the student saves per month. To do this, the number of cigarette packages she smokes is multiplied by the price she pays for them.

Per month: 15 packs*$7 each packet=$105

This means that per month she save $ 105.

Now you must determine the amount of money saved per year, knowing that in a year there are 12 months. Therefore, you make a simple rule of three: If in a month you save $ 105, how much money do you save in 12 months?

Per year: $\frac{105*12months}{1 month} =1260$

This means that per year she save $ 1260. And she each month invests the amount she would have spent on cigarettes in a savings plan that averages a 4% annual return. This means that in addition to saving $ 1260 per year, she gets 4% annually. For this you must first know how much 4% equals. For that you must keep in mind that to obtain a percentage in decimals, you must divide by 100. Then 0.04 represents 4%.

Now, to get the annual return of the savings plan you multiply the percentage by the amount invested in the plan. And to determine the total amount of money she save in a year with this plan, you add the amount invested plus the annual return. All this is:

0.04*$1260+$1260=$1310.4

This means that finally per year she save $ 1310.4 with the annual return.

You know that between 65 and 21 years of age of the student, there is a difference of 44 years, obtained by calculating 65 years minus 21 years. Then you can make a simple rule of three to determine the amount of money saved during those 44 years:if in one year the student save $1310. 4, how much money do she save in 44 years?

$\frac{1310.4*44 years}{1 year} =57657.6$

So, finally, she will have saved $ 57657.6 by the time she is 65