# Help with a homework question calculating interest

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!

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

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