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gmatophobia
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In a certain retirement program, benefits are based on retiring at age 08 Jan 2024, 12:36
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66% (02:39) correct 34% (03:02) wrong based on 673 sessions

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In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00
B. $250.00
C. $235.60
D. $206.67
E. $186.00

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Bunuel
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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 08:21
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saurabhbajpai
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00
B. $250.00
C. $235.60
D. $206.67
E. $186.00

How do we know that we are not solving for compound interest here?

Posted from my mobile device

The calculation is based on simple interest, rather than compound interest, as the increase is consistently applied to the original amount, not to the accumulating balance:

...the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65.

So, if the monthly payment was x, then for each month worked after age 62 until age 65, it would increase by 2/3 of 1 percent of x each month. This means the payment increases by (2/3) * (1/100) * x for each month worked after age 62.

If it were compound interest, the wording might be:

In a certain retirement program, benefits are based on retiring at age 62. However, if retirement is delayed, the monthly payment increases by 2/3 of 1 percent each month, compared to the previous month's payment, for each additional month worked after age 62 until age 65.
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In a certain retirement program, benefits are based on retiring at age 08 Jan 2024, 20:04
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gmatophobia
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by \(\frac{2}{3}\) of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00

B. $250.00

C. $235.60

D. $206.67

E. $186.00

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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 01:09
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Can someone please explain this?
Bunuel karishma chetan2u

I am facing difficulty converting the word problem to numbers.
Particularly the 2/3 of 1% part.
The solution posted earlier is a good breakdown but I am afraid I need more help.
Thanks
KarishmaB
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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 01:59
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VivekPrateek
gmatophobia
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by \(\frac{2}{3}\) of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00

B. $250.00

C. $235.60

D. $206.67

E. $186.00

Show Spoiler
Attachment:
Screenshot 2024-01-09 005617.png

Posted from my mobile device

108×3 doesn't equal 124
108×3 equals 324
Why this post is so misleading but still got the answer right?

Doesn't this question need compound interest formula? Which is not appropriate for PS problem imo.
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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 02:27
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gmatophobia
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by \(\frac{2}{3}\) of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00

B. $250.00

C. $235.60

D. $206.67

E. $186.00

Show Spoiler
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Screenshot 2024-01-09 005617.png

Let the monthly payment be x, if someone retires at 62 yrs of age. However, the monthly payment keeps increase by \frac{2}{3}[/m] of 1 percent each month spent extra.

\(\frac{2}{3}\) of 1 percent would mean just \(\frac{2}{3}\) * 1 percent or simply \(\frac{2}{3}\) percent

Thus, 3 yrs or 36 months would be mean an excess of \(\frac{2}{300}*x*36\) or \(\frac{24x}{100}\).
Thus the monthly payment after 65 years becomes \(x+\frac{24x}{100}=\frac{124x}{100}=310\)

\(x=\frac{310*100}{124}=\frac{31*10*100}{31*4}=250\)
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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 02:34
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sanebeyondone
VivekPrateek
gmatophobia
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by \(\frac{2}{3}\) of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00

B. $250.00

C. $235.60

D. $206.67

E. $186.00

Show Spoiler
Attachment:
Screenshot 2024-01-09 005617.png

Posted from my mobile device

108×3 doesn't equal 124
108×3 equals 324
Why this post is so misleading but still got the answer right?

Doesn't this question need compound interest formula? Which is not appropriate for PS problem imo.

Yes, the mistake is: it is 100% + 8% for each year, so 100+8*3 or 124%.

Secondly, the question of talks of retirement benefits as say x.
For each extra month served, the person gets 2/3 of 1 percent of x. Thus, it is simple interest.
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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 07:10
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How do we know that we are not solving for compound interest here?

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In a certain retirement program, benefits are based on retiring at age 24 Jan 2024, 09:20
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gmatophobia
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00
B. $250.00
C. $235.60
D. $206.67
E. $186.00

Show Spoiler
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Screenshot 2024-01-09 005617.png

The monthly payment is increased by 2/3, so yearly (2/3)*12=8%. Therefore in 3 years it becomes 8*3=24%.
Let, at 62, his monthly payment was $x. So, after 3 years it becomes x*(1 + 24/100)=310.
Solving, we get x=$250(B).
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In a certain retirement program, benefits are based on retiring at age 21 May 2025, 11:37
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KarishmaB

Found this in mock test 5, could you please help. The language of the question threw me off. please share in detail how we translate "the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65" into a mathematical form
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In a certain retirement program, benefits are based on retiring at age 21 May 2025, 12:13
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tgmat24
In a certain retirement program, benefits are based on retiring at age 62, but if retirement is delayed, the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65. If Mr. Johnson would receive a monthly payment of $310 by starting benefits on his 65th birthday, what would the monthly payment be if he started on his 62nd birthday?

A. $286.00
B. $250.00
C. $235.60
D. $206.67
E. $186.00

Found this in mock test 5, could you please help. The language of the question threw me off. please share in detail how we translate "the monthly payment is increased by 2/3 of 1 percent for each month worked after age 62 until age 65" into a mathematical form

That phrasing means the increase is 2/3 of 1%, or simply 2/3%, of the original payment for each month worked after age 62. So if the original payment is x and someone worked n months beyond age 62, the cumulative increase would be n * (2/3)% * x, making the total payment after n months equal to x + n * (2/3)% * x.

We’re told that after 36 months, the payment is $310, so x + 36 * (2/3) * (1/100) * x = 310, which gives x = 250.

Hope it's clear.
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In a certain retirement program, benefits are based on retiring at age 29 May 2025, 16:02
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Why are we not able to use 310 x 76/100? I got 235.60.
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In a certain retirement program, benefits are based on retiring at age 29 May 2025, 23:57
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ravjaz
Why are we not able to use 310 x 76/100? I got 235.60.
The 24% is the increase from the original payment, so the correct setup is original payment * 1.24 = 310.

If you do 310 * 76/100, you're wrongly assuming that the original payment is 76% of the total payment, which is not the same thing. For example, if you increase something by 20%, you won’t get the original by multiplying the result by 0.8, you should divide the final amount by 1.2.
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In a certain retirement program, benefits are based on retiring at age 06 Jun 2025, 04:24
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Bunuel please tell how to determine this?

saurabhbajpai
How do we know that we are not solving for compound interest here?

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In a certain retirement program, benefits are based on retiring at age 06 Jun 2025, 06:22
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shubhim20
Bunuel please tell how to determine this?

saurabhbajpai
How do we know that we are not solving for compound interest here?

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