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At her current job, Mary gets a 1.5% raise twice per year. Which of th

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Bunuel
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At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   19 Aug 2018, 09:49
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At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?


(A) \(s(1.5)^{2y}\)

(B) \(s(0.015)^{2y}\)

(C) \(s(1.015)^{2y}\)

(D) \(s(1.5)\frac{y}{2}\)

(E) \(s(1.015)\frac{y}{2}\)
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   19 Aug 2018, 10:29
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Bunuel wrote:
At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?


(A) \(s(1.5)^{2y}\)

(B) \(s(0.015)^{2y}\)

(C) \(s(1.015)^{2y}\)

(D) \(s(1.5)\frac{y}{2}\)

(E) \(s(1.015)\frac{y}{2}\)


1.5% rise is equivalent to s*\((1+\frac{1.5}{100})=s*(1+0.015)=s*1.015\)
Mary’s current income y years after starting the job=\(s(1.015)^{2y}\) (Since income increases twice a year)

Ans. (C)
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BrentGMATPrepNow
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   12 Feb 2019, 10:40
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Bunuel wrote:
At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?


(A) \(s(1.5)^{2y}\)

(B) \(s(0.015)^{2y}\)

(C) \(s(1.015)^{2y}\)

(D) \(s(1.5)\frac{y}{2}\)

(E) \(s(1.015)\frac{y}{2}\)


One approach here is to apply the COMPOUND INTEREST formula.
However, if you didn't see that the question is analogous to a COMPOUND INTEREST question, we can also solve the question by looking for a pattern.

Let's try that:

Time elapsed (in years) | salary
0 | s
0.5 | (1.015)(s)
1 | (1.015)(1.015)(s)= (1.015)²(s) =
1.5 | (1.015)(1.015)(1.015)(s) = (1.015)³(s) =
2 | (1.015)⁴(s)
2.5 | (1.015)⁵(s)
3 | (1.015)⁶(s)
3.5 | (1.015)⁷(s)
4 | (1.015)⁸(s)
.
.
.
See the pattern???
.
.
.
y | (1.015)^2y(s)

Answer: C

Cheers,
Brent
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   05 Nov 2020, 17:00
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Bunuel wrote:
At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?


(A) \(s(1.5)^{2y}\)

(B) \(s(0.015)^{2y}\)

(C) \(s(1.015)^{2y}\)

(D) \(s(1.5)\frac{y}{2}\)

(E) \(s(1.015)\frac{y}{2}\)


Solution:

We can use the compound interest formula A = P(1 + r)^n to solve the problem (note: P is the principal, or initial value, n is the number of compounding periods, r is the interest rate per period and A is the final value). Here, P = s, n = 2y, and r = 1.5% = 0.015. Therefore, the final value is:

A = s(1 + 0.015)^(2y) = s(1.015)^(2y)

Answer: C
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   12 Aug 2022, 01:26
BrentGMATPrepNow wrote:
Bunuel wrote:
At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?


(A) \(s(1.5)^{2y}\)

(B) \(s(0.015)^{2y}\)

(C) \(s(1.015)^{2y}\)

(D) \(s(1.5)\frac{y}{2}\)

(E) \(s(1.015)\frac{y}{2}\)


One approach here is to apply the COMPOUND INTEREST formula.
However, if you didn't see that the question is analogous to a COMPOUND INTEREST question, we can also solve the question by looking for a pattern.

Let's try that:

Time elapsed (in years) | salary
0 | s
0.5 | (1.015)(s)
1 | (1.015)(1.015)(s)= (1.015)²(s) =
1.5 | (1.015)(1.015)(1.015)(s) = (1.015)³(s) =
2 | (1.015)⁴(s)
2.5 | (1.015)⁵(s)
3 | (1.015)⁶(s)
3.5 | (1.015)⁷(s)
4 | (1.015)⁸(s)
.
.
.
See the pattern???
.
.
.
y | (1.015)^2y(s)

Answer: C

Cheers,
Brent


BrentGMATPrepNow hey Brent if it is compound interest formula then why you didnt divide 0.015 by 2. compounding occurs twice a year.

.. isnt it a compound interest formula \(A = P (1+\frac{r}{n})^{nt}\) where

A is total amount with accrued percent
P is principal amount
R is interest rate
n is number of compounding per year :)
t is number of years
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BrentGMATPrepNow
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   12 Aug 2022, 07:35
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dave13 wrote:
BrentGMATPrepNow hey Brent if it is compound interest formula then why you didnt divide 0.015 by 2. compounding occurs twice a year.

.. isnt it a compound interest formula \(A = P (1+\frac{r}{n})^{nt}\) where

A is total amount with accrued percent
P is principal amount
R is interest rate
n is number of compounding per year :)
t is number of years


If the question says "Mary gets a 1.5% raise twice per year"
So, every 6 months, she gets a 1.5% raise.

Compare this to an official question (https://gmatclub.com/forum/john-deposit ... 35825.html) that says "John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly."
Here we are given the annual percent interest, which is compounded quarterly, which means we must divide 4% by 4.

Does that help?
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink] New post   13 Mar 2024, 04:24
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Re: At her current job, Mary gets a 1.5% raise twice per year. Which of th [#permalink]
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