In a certain retirement program, benefits are based on retiring at age

Question

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

Bunuel · Accepted Answer

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.

VivekSri · Answer

Posted from my mobile device

sanebeyondone · Answer

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.

chetan2u · Answer

Let the monthly payment be x, if someone retires at 62 yrs of age. However, the monthly payment keeps increase by \frac{2}{3}  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

chetan2u · Answer

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.

saurabhbajpai · Answer

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

Posted from my mobile device

samarpan.g28 · Answer

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).

tgmat24 · Answer

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

Bunuel · Answer

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.

ravjaz · Answer

Why are we not able to use 310 x 76/100? I got 235.60.

Bunuel · Answer

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.

xyzKunal · Answer

This is rather a simple question but with strong wordings.

2/3 of 1% is nothing but 0.66%.

Question says, 0.66% is increased every month ( Means Simple Addition , not compounding)

Now, he worked for 36 months Extra(3 years)
So, total addition (increase) in monthly Payment =  36*0.66% = 24%.

Now, Let's assume initial Payment was X
so,  X + 24% of X  = 310
=>1.24X = 310
=> X= 310/1.24 =  250

shaliny · Answer

hii
 here $310 is a monthly payment on 65th birthday then it should be equal to increment for 1 month, why it is equal to increment to all 36 month, not clear
please help

Bunuel · Answer

Because $310 is the final monthly payment after all 36 months of increases have been applied . It’s not the result of just one month’s increment, it’s the result of 36 separate increments added to the base amount from age 62. Please check these posts: https://gmatclub.com/forum/in-a-certain ... l#p3572512 https://gmatclub.com/forum/in-a-certain ... l#p3575762

SharukhB · Answer

I solved it under 2 mins by the following method:

No. of years worked beyond the age of 62 = 3 years = 36 months

Additional % of pay out to Mr. Johnson is calculated by the formula 2/3 X 1/100 X 36 =0.24

That means the amount of $ 310 is 124% of his original pay so we can find out what is 100% i.e. 310 / 1.24 = 250$ so B

RockoGmat · Answer

x-> initial monthly payment he would get in the case where it would have started at the age of 62

x + 2/3 * 1/100 * x * 36 (12 * 3 months) = 310

31x/25 = 310

x=250

In a certain retirement program, benefits are based on retiring at age

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a certain retirement program, benefits are based on retiring at age

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards