Question

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?

Answer 1

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.

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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