A certain car's price decreased by 2.5% (from the original price) each

Question

A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100

CounterSniper · Answer

1996 to 2002 = 6 years
in one year depreciation is 2.5% (note from original price) 
which is $550
in 6 years total depreciation = 550*6 =$3300
increase in car price = $1500
car price in 2002 = 22000+1500-3300= $20200

Divyadisha · Answer

Important point to notice- 2.5% decrease from the original price

2.5% of 22,000= 550

Total reduction in 6 years= 550*6= 3300

Final price= 22,000 +1500 - 3300= 20,200

C is the answer

OptimusPrepJanielle · Answer

Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500

Net price of the car in 02 = 18700 + 1500 = $20200

Correct Option: C

adiagr · Answer

Reduction: 2.5 % from original price

(2.5/100) * 22000 = 550.

6 * 550 = Rs. 3300 reduction.

Increase: Rs, 1500

Final price: 22000 - 3300 + 1500 = 22000 - 1800 = 20200.

C is the answer.

manishtank1988 · Answer

Unless i am not reading the question properly, it is not mentioned that we have to use simple interest AND NOT COMPOUND interest. Am i overthinking?
I did following:
Final Price = P(1-r/100)^t
= 22000(1-25/1000)^7
= 22000(1-1/40)^7
= 22000 (1 - 7/40) Binomial short-cut
= 22000*33/40
= 550*33 = 11*50*3*11 = 121*150 = 18150
Adding cost to final price = 18150+1500 = 19650 => thus B

So in exam, like here (SC - focusing on similarity :lol:

), if it is not mentioned SI or CI we should use SI?

), if it is not mentioned SI or CI we should use SI?

ks11 · Answer

A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100
---------------------------------------------------
Number of years from 1996 to 2002 = 6
Price of the car in 1996 = $22,000
Price decreased each year by 2.5%

We know that the price decreased 6 times @ 2.5% each year as the number of years from 1996 to 2002 is 6
Therefore, in place of going for lengthy and complicated calculation just multiply 2.5 with 6 -
 2.5 * 6 = 15
Now, calculate 15% of $22,000
 15/100 * 22,000 = $3300
Price of the car after decreasing the price for continuous 6 years @ 2.5% 
 = Price of Car in year 1996 (Initial Price) - Price decreased in 6 years
 = $22,000 - $3300
 = $18700

It is mentioned that the car's price increased by $1,500 with the investment in a new carburetor and a new audio system for the car
therefore, the final price of the car in year 2002 is -
 = $18,700 + 1,500
 = $20,200

Answer is 'C'

kaloochand · Answer

hi, can someone tell me why we have used the simple interest formula and not the compound interest formula because to me it seems like a problem that needs compound interest formula

Bunuel · Answer

The key is in the wording:  "from the original price."  That means the car loses  2.5% of $22,000 each year , not 2.5% of its current value.

So this is not compound depreciation. It's a fixed amount each year:

2.5% of 22,000 = 550 dollars lost per year.

Over 6 years, total depreciation = 550 * 6 = 3,300.

Then, add back the $1,500 increase from upgrades.

Final value = 22,000 - 3,300 + 1,500 =  $20,200 .

Answer: C.

Prabhjas10 · Answer

Hi, if you read the question, it's mentioned the price decreases each year "from the original price", what this means is that the interest is same per year i.e. 2.5% of 22000(i.e. only your base price earns/loses interest), however suppose the interest were to be compounded then in that case the interest would not be the same, it would've kept on compounding on it's self, each cycle ( i.e. your base price earns/loses interest + your interest would earn/lose interest).

Hope this helps.

kaloochand

hi, can someone tell me why we have used the simple interest formula and not the compound interest formula because to me it seems like a problem that needs compound interest formula

Hope this helps.

DyutiB · Answer

How did you get this -

= 22000(1-1/40)^7 
 = 22000 (1 - 7/40)  Binomial short-cut
   
What is binomial short cut?

A certain car's price decreased by 2.5% (from the original price) each

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A certain car's price decreased by 2.5% (from the original price) each

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