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# On January 1, 1994, Jill invested P dollars in an account that pays in

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Senior Manager
Joined: 19 Oct 2012
Posts: 335

Kudos [?]: 59 [0], given: 103

Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
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WE: Information Technology (Computer Software)
On January 1, 1994, Jill invested P dollars in an account that pays in [#permalink]

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17 Oct 2017, 06:33
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Difficulty:

15% (low)

Question Stats:

79% (00:39) correct 21% (00:45) wrong based on 80 sessions

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On January 1, 1994, Jill invested P dollars in an account that pays interest at a rate of 8 percent per year, compounded annually on December 31. If there were no other deposits or withdrawals in the account, how many dollars were in the account on January 1, 1998, in terms of P?
A) $$0.32P$$
B) $$4.32P$$
C) $$(0.08)^4P$$
D) $$(1.08)^4P$$
E) $$(1.08P)^4$$
[Reveal] Spoiler: OA

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Kudos [?]: 59 [0], given: 103

Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [0], given: 39

Location: India
GPA: 3.82
Re: On January 1, 1994, Jill invested P dollars in an account that pays in [#permalink]

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17 Oct 2017, 11:51
TheMechanic wrote:
On January 1, 1994, Jill invested P dollars in an account that pays interest at a rate of 8 percent per year, compounded annually on December 31. If there were no other deposits or withdrawals in the account, how many dollars were in the account on January 1, 1998, in terms of P?
A) $$0.32P$$
B) $$4.32P$$
C) $$(0.08)^4P$$
D) $$(1.08)^4P$$
E) $$(1.08P)^4$$

Between 1st Jan 1994 & 1st Jan 1998, time elapsed = 4 years

Use the Compound interest formula to calculate the amount

$$A=P(1+\frac{r}{100})^n$$ $$=> P(1+\frac{8}{100})^4$$

or $$A=P(1.08)^4$$

Option D

Kudos [?]: 304 [0], given: 39

VP
Joined: 22 May 2016
Posts: 1106

Kudos [?]: 396 [0], given: 640

On January 1, 1994, Jill invested P dollars in an account that pays in [#permalink]

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17 Oct 2017, 12:20
TheMechanic wrote:
On January 1, 1994, Jill invested P dollars in an account that pays interest at a rate of 8 percent per year, compounded annually on December 31. If there were no other deposits or withdrawals in the account, how many dollars were in the account on January 1, 1998, in terms of P?
A) $$0.32P$$
B) $$4.32P$$
C) $$(0.08)^4P$$
D) $$(1.08)^4P$$
E) $$(1.08P)^4$$

Knowing the formula for compound interest helps a lot here.

Compound interest is given by

$$A = P(1 +\frac{r}{n})^{nt}$$

A = final amount
P = principal invested
r = interest rate in decimal form
n = number of compounding periods per year
t = time

Here interest compounds annually; it earns "interest on interest," and pays one time per year, on December 31.

So r = .08
Because $$n = 1$$, $$(\frac{.08}{1}) = .08$$

Then $$1 + .08 = 1.08$$

Time t, = 4 years: she gets paid December 31 of 1994, 1995, 1996, and 1997

Where n = 1 and t = 4, thus: $$(1.08)^{1*4} = (1.08)^4$$

Finally, multiply by the principal: $$P(1.08)^4$$

Kudos [?]: 396 [0], given: 640

Target Test Prep Representative
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Re: On January 1, 1994, Jill invested P dollars in an account that pays in [#permalink]

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19 Oct 2017, 10:16
TheMechanic wrote:
On January 1, 1994, Jill invested P dollars in an account that pays interest at a rate of 8 percent per year, compounded annually on December 31. If there were no other deposits or withdrawals in the account, how many dollars were in the account on January 1, 1998, in terms of P?
A) $$0.32P$$
B) $$4.32P$$
C) $$(0.08)^4P$$
D) $$(1.08)^4P$$
E) $$(1.08P)^4$$

Since the investment of P dollars was compounded annually for 4 years, the new value of the original investment is P(1.08)^4.

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Kudos [?]: 1010 [0], given: 3

Re: On January 1, 1994, Jill invested P dollars in an account that pays in   [#permalink] 19 Oct 2017, 10:16
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