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Question : Imagine that you deposit $6,000 a year, starting one year from today, for four years into a savings account paying 6% per annum. (That is one deposit of $6,000 per year.) How much money will you have immediately after you make your fourth and final deposit?

The answer I got was 25,274.18

The work was

6000/.06(1-(1+.06)^-5) = 25,274.18

I also tried this

6000/.06(1-(1+.06)^-4)= 20790.63

Both of them were incorrect. I really appreciate the help in advance. Thank you very much!

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Your second calculation would be correct if you were asked for the present value of the deposits. For the future value, you have 4 deposits, the first of which compounds for 3 years and the last for 0 years. Thus, FV = $6,000 * sum(i=0..3) 1.06^i = $6,000 * (1.06^4 - 1) / 0.06 = $26,247.70

  • Thank you for the help, I am not sure where you get the sum(i=0..3), or where the i comes from . This part makes sense to me $6,000 * (1.06^4 - 1) / 0.06 = $26,247.70 – daniel blanco Jun 30 at 0:02
  • See here. The i is a "dummy variable", and sum(i=0..3) 1.06^i is just a compact way of writing 1.06^0 + 1.06^1 + 1.06^2 + 1.06^3. – nanoman Jun 30 at 0:10
  • Thank you very much for the explanation, that was very clear and thorough. I really appreciate the help. – daniel blanco Jun 30 at 5:18
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When I'm stumped, I break problems down into their constituent parts, and since it's been 35 years since I took a finance course, that's what I'm doing here:

Year    Yearly:
  0     6000*1.06^4 =  7574.86
  1     6000*1.06^3 =  7146.10
  2     6000*1.06^2 =  6741.60
  3     6000*1.06^1 =  6360.00
  4     6000*1.06^0 =  6000.00
              Total = 33822.56

The correct answer I think depends on whether or not there's a final deposit.

  • The question is explicit that there is a final deposit, but that there is no initial deposit now ("starting one year from today"). You should remove the "Year 0" entry. – nanoman Jun 29 at 23:30
  • Thank you RonJohn for writing that out for me, and nanoman for correcting it. – daniel blanco Jun 29 at 23:57
  • @nanoman and OP: whether or not money is being deposited now, it's still "for four years". If the teacher meant "ending four years from now" then IMO it's confusingly written. – RonJohn Jun 30 at 0:12

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