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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
On January 1, 1994, Jill invested P dollars in an account that pays in
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25 Jan 2023, 00:03
25 Jan 2023, 00:03
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Question Stats:
66% (00:53) correct
33% (04:15) wrong based on 3 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) \((1.08P)^4\)
(A) \(0.32P\)
(B) \(4.32P\)
(C) \((0.08)^4P\)
(D) \((1.08)^4P\)
(E) \((1.08P)^4\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: On January 1, 1994, Jill invested P dollars in an account that pays in
[#permalink]
27 Jan 2023, 11:18
27 Jan 2023, 11:18
1
Expert Reply
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: \(P(1.08)^4\)
Answer: D
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: \(P(1.08)^4\)
Answer: D
gmatclubot
Re: On January 1, 1994, Jill invested P dollars in an account that pays in [#permalink]
27 Jan 2023, 11:18
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