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# Jack deposited p dollars into a new account that earned 4 percent annu

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Math Expert
Joined: 02 Sep 2009
Posts: 53791
Jack deposited p dollars into a new account that earned 4 percent annu  [#permalink]

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01 Oct 2018, 22:47
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Difficulty:

15% (low)

Question Stats:

86% (02:03) correct 14% (01:56) wrong based on 25 sessions

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Jack deposited p dollars into a new account that earned 4 percent annual interest compounded annually. A year later he deposited additional p dollars in the account. If there were no other transactions and if the account showed q dollars at the end of the two years, which of the following expresses p in terms of q?

(A) q/(1 + 1.04)

(B) q/(1.04 + 1.08)

(C) q/(1.08 + 1.12)

(D) q/(1.04 + 1.04^2)

(E) q/(1.04^2 + 1.04^3)

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Re: Jack deposited p dollars into a new account that earned 4 percent annu  [#permalink]

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02 Oct 2018, 04:55
Bunuel wrote:
Jack deposited p dollars into a new account that earned 4 percent annual interest compounded annually. A year later he deposited additional p dollars in the account. If there were no other transactions and if the account showed q dollars at the end of the two years, which of the following expresses p in terms of q?

(A) q/(1 + 1.04)

(B) q/(1.04 + 1.08)

(C) q/(1.08 + 1.12)

(D) q/(1.04 + 1.04^2)

(E) q/(1.04^2 + 1.04^3)

If the amount deposited into Jack's account is $$p$$, and a 4% interest has been compounded annually,
the amount in Jack's account after a year will be $$1.04p$$. After a year, another $$p$$ dollars is added to
the account and the total compound interest is $$1.04(1.04p) + 1.04p$$ = $$(1.04)^2*p + 1.04p$$

The total amount at the end of 2 years in Jack's account is $$q$$ which also equals $$p(1.04 + (1.04)^2)$$

Therefore, p expressed in terms of q can be written as $$\frac{q}{(1.04 + 1.04^2)}$$ (Option D)
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Re: Jack deposited p dollars into a new account that earned 4 percent annu   [#permalink] 02 Oct 2018, 04:55
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