Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
a: w/1+1.08
b: w/1.08+1.16
c: w/1.16+1.24
d: w/1.08+1.08^2
e: w/1.08^2+1.08^2
my approach is :
deposit is x:
(1.08){x(1+0.08)}=w, then x=w/1.16*1.08
Am I missing anything here?? Pls explain....
No, No, I calculate in a wrong way, I chose B~~!!!! Pls explain in details and give me a full calculation process!!! Thank you
A math prob, pls help
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Last edited by tracyyahoo on Mon Oct 03, 2011 10:34 pm, edited 2 times in total.
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At the end of 2 years you have
w = 1.08(1.08x) + 1.08x
1.08(1.08x) - 8% interest on amount after first year
1.08x - Interest on 'x' deposited the second year.
so,
x = w/1.08+1.08^2 D
PS: your equation (1.08){x(1+0.08)}=w
It shoud be (1+1.08) and not (1 + 0.08)
w = 1.08(1.08x) + 1.08x
1.08(1.08x) - 8% interest on amount after first year
1.08x - Interest on 'x' deposited the second year.
so,
x = w/1.08+1.08^2 D
PS: your equation (1.08){x(1+0.08)}=w
It shoud be (1+1.08) and not (1 + 0.08)
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Hi All,
We're told that Alex deposited X dollars into a new account that earned 8 percent annual interest, compounded annually and 1 year later Alex deposited an additional X dollars into the account. We're asked - if there were no other transactions and if the account contained W dollars at the end of 2 years, which of the following expresses X in terms of W. This question can be solved by TESTing VALUES.
Let's start with X = $100
After 1 year, this $100 would earn 8% interest --> $100 + $8 = $108 after 1 year
Then Alex deposits another $100 --> $108 + $100 = $208
After 1 year, this $208 would earn 8% interest --> $208 + $16.64 = $224.64 after 2 years
Thus, we're looking for an answer that equals 100 when W=224.64 is inserted.
While the answers might 'look complex', we're ultimately looking for one that has a denominator equal to 2.2464 (since that's what we'd have to divide our W by to get to 100). You can eliminate 3 answers immediately (Answers A, B and C won't give you that exact denominator). By calculating either of the remaining two answers, you'll know that you either have the correct answer OR you don't - and the other answer will be the correct answer...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that Alex deposited X dollars into a new account that earned 8 percent annual interest, compounded annually and 1 year later Alex deposited an additional X dollars into the account. We're asked - if there were no other transactions and if the account contained W dollars at the end of 2 years, which of the following expresses X in terms of W. This question can be solved by TESTing VALUES.
Let's start with X = $100
After 1 year, this $100 would earn 8% interest --> $100 + $8 = $108 after 1 year
Then Alex deposits another $100 --> $108 + $100 = $208
After 1 year, this $208 would earn 8% interest --> $208 + $16.64 = $224.64 after 2 years
Thus, we're looking for an answer that equals 100 when W=224.64 is inserted.
While the answers might 'look complex', we're ultimately looking for one that has a denominator equal to 2.2464 (since that's what we'd have to divide our W by to get to 100). You can eliminate 3 answers immediately (Answers A, B and C won't give you that exact denominator). By calculating either of the remaining two answers, you'll know that you either have the correct answer OR you don't - and the other answer will be the correct answer...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich