You want to go to grad school 4 years from now, and you can save $5,000 per year, beginning one year from today. you plan to deposit the funds in a mutual fund which you expect to return 10% per year. under these conditions, how much will you have just after you make the 4th deposit, 4 years from now?

The value of the final deposit is 5000. The value of the one a year previously is 5000*1.1 = 5500. The one previous to that has a value of 5000*1.1^2 = 6050. The first deposit has a value of 5000*1.1^3 = 6655.

The total value of the 4 deposits is
.. 6665 +6050 +5500 +5000 = 23,205

You will have $23,205 just after you make the 4th deposit.


This is the sum of 4 terms of a geometric sequence with common ratio 1.1 and initial value 5000. That can be calculated as
.. a0*(r^n -1)/(r -1)
.. 5000*(1.1^4 -1)/(1.1 -1)
.. = 5000*4.641
.. = 23,205

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.