Banking (annual interest over 5yrs)

[TiredBu]

I'm trying to figure out the best option and I figured what better place to ask my question here!

Question : I have lets say $10,000 that pays 8% interest compounded annually. If to that account, I deposit 5k at the end of each year for 5 years, how much will I have after the last deposit?

Now.. I'm confused because I got 2 different answers, which make (some) sense:

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1. (My first answer + the work)
End of Year 1 = $16,200 = ($10,000+$5,000)*1.08
End of Year 2 = $22,896 = ($16,200+$5,000)*1.08
End of Year 3 = $30,127.68 = ($22,896+$5,000)*1.08
End of Year 4 = $37,937.8944 = ($30,127+$5,000)*1.08
End of Year 5 = $46,372.92595 = ($37,937.8944+$5,000)*1.08

2. (My second answer + the work)
$5,000*[((1.08^6)-1)/0.08] = $36,679.64518
$36,679.64518 + $10,000 = $46,679.64518

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Both of these seem relatively correct... However I'm not even sure :/

Help me figure out which of my 2 conclusions are correct or if I even did it right in the first place! >.<

 

[TiredBu]

Arg! That's so frustrating, the slightest mistake makes for a convoluted experience... :s

Thanks though JeffM for pointing out the errors. (Time to pound that into my head -.- !)

 

[TchrWill]

I'm trying to figure out the best option and I figured what better place to ask my question here!

Question : I have lets say $10,000 that pays 8% interest compounded annually. If to that account, I deposit 5k at the end of each year for 5 years, how much will I have after the last deposit?

Assuming that the annual $5000 deposits combine with the initial deposit of $10,000 to draw 8% compounded annually.

Beginning of year 1: $10,000
End of year 1: 10,000(1.08) + 5000 = $15,800 (or start of year 2)
End of year 2: 15,800(1.08) + 5000 = $22,064
End of year 3: 22,064(1.08) + 5000 = 28,829.12
End of year 4: 28,829.12(1.08) + 5000 = $36,135.45
End of year 5: 36,135.45(108( + 5000 = $44,026.28

Alternatively:
10,000(1.08)^5 + 5000[(1.08)^5 - 1]/.08 = 14,693.28 + 29,333 = $44,026.28

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Assuming that the annual $5000 deposits combine with the initial deposit of $10,000 to draw 8% compounded annually.

Beginning of year 1: $10,000
End of year 1: 10,000(1.08) + 5000 = $15,800 (or start of year 2)
End of year 2: 15,800(1.08) + 5000 = $22,064
End of year 3: 22,064(1.08) + 5000 = 28,829.12
End of year 4: 28,829.12(1.08) + 5000 = $36,135.45
End of year 5: 36,135.45(108( + 5000 = 44,026.28

Alternatively:
10,000(1.08)^5 + 5000[(1.08)^5 - 1]/.08 = 14,693.28 + 29,333 = $44,026.28



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