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01 Mar 2022, 03:00
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E
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Difficulty:
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Question Stats:
79% (01:40) correct
21%
(01:47)
wrong
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A certain account pays 1.5 percent compound interest every 3 months. A person invested an initial amount and did not invest any more money in the account after that. If after exactly 5 years, the amount of money in the account was T dollars, which of the following is an expression for the original number of dollars invested in the account?
A. \((1.015)^4T\)
B. \((1.015)^{15}T\)
C. \((1.015)^{20}T\)
D. \(\frac{T}{(1.015)^{15}}\)
E. \(\frac{T}{(1.015)^{20}}\)
A. \((1.015)^4T\)
B. \((1.015)^{15}T\)
C. \((1.015)^{20}T\)
D. \(\frac{T}{(1.015)^{15}}\)
E. \(\frac{T}{(1.015)^{20}}\)
01 Mar 2022, 12:01
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Bunuel
A certain account pays 1.5 percent compound interest every 3 months. A person invested an initial amount and did not invest any more money in the account after that. If after exactly 5 years, the amount of money in the account was T dollars, which of the following is an expression for the original number of dollars invested in the account?
A. \((1.015)^4T\)
B. \((1.015)^{15}T\)
C. \((1.015)^{20}T\)
D. \(\frac{T}{(1.015)^{15}}\)
E. \(\frac{T}{(1.015)^{20}}\)
A. \((1.015)^4T\)
B. \((1.015)^{15}T\)
C. \((1.015)^{20}T\)
D. \(\frac{T}{(1.015)^{15}}\)
E. \(\frac{T}{(1.015)^{20}}\)
Breaking Down the Info:
\(1.5\%\) compound interest means we are multiplying the original amount by \(101.5\%\) every three months. After 5 years, we have 20 periods of 3-months, so the multiplying factor is \(1.015^{20}\).
Note that T is the resulting amount, however, so in order to find the principal we should divide by the factor above.
Answer: E
amilstein
Joined: 22 Jan 2019
Last visit: 02 Oct 2023
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Location: United States
Schools: Tuck '25 (D) Yale '25 (WL) Stern '25 (A$$$$) Kellogg '25 (M$$$) HBS '25 (D) Stanford '25 (D) Sloan '25 (D)
GMAT 1: 650 Q39 V40
GMAT 2: 690 Q42 V42
GMAT 3: 700 Q47 V40
GMAT 4: 730 Q47 V44
GPA: 3.97
Schools: Tuck '25 (D) Yale '25 (WL) Stern '25 (A$$$$) Kellogg '25 (M$$$) HBS '25 (D) Stanford '25 (D) Sloan '25 (D)
GMAT 4: 730 Q47 V44
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05 Aug 2022, 09:51
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shouldn't the interest of 1.5% compounded every three months be calculated as P(1+.015/4)^20=T?
