If a town of 25,000 people is growing at a rate of approximately 1

Question

If a town of 25,000 people is growing at a rate of approximately 1 percent per year, the population of the town in 5 years will be closest to

A. 26000
B. 27000
C. 28000
D. 29000
E. 30000

PS07046

soloveva · Accepted Answer

To calculate (1.01)^5* 25 000 is indeed a bad idea, especially on a gmat test day:)

How can we quickly estimate the closest value of this expression? 
Compound interest gives a greater growth because it is "an interest of interests".
We can easily calculate the amount after five years for a  simple interest : 25 000* (1.01*5)=26 250. The increase=26 250- 25 000=1 250.
Thus, the compound interest should increase by lower than 0.01*(1 250)*4=50 (the compound interest becomes different from simple interest beginning with the 2nd year, thus, 5-1=4).
The increase with the compound interest rate will be lower that 26 250+ 50=26 300, which is closer to 26 000. So A.

mcelroytutoring · Answer

This question is quite easy, but it appears difficult if we focus too much on the formula, and the fact that it is difficult to execute 1.01^5 without a calculator. Beware of "formula tunnel vision": instead of worrying about how to calculate the answer using the interest formula, we should instead understand that a 1 percent increase is really quite easy to calculate by hand (just remove the final two digits of the original number, and then add it to the original number):

Year 1: 25,000 + 1% = 25,000 + 250 = 25,250

Year 2: 25,250 + 1% = 25,250 + 252 = 25,502

Year 3: 25,502 + 1% = 25,502 + 255 = 25,757

Year 4: 25,757 + 1% = 25,757 + 257 = 26,014

Year 5: 26,014 + 1% = 26,014 + 260 = 26,274

Thus the answer is closest to Choice A (26,000).

Year 1: 25,000 + 1% = 25,000 + 250 = 25,250

Year 2: 25,250 + 1% = 25,250 + 252 = 25,502

Year 3: 25,502 + 1% = 25,502 + 255 = 25,757

Year 4: 25,757 + 1% = 25,757 + 257 = 26,014

Year 5: 26,014 + 1% = 26,014 + 260 =  26,274

Thus the answer is closest to  Choice A  (26,000).

NoHalfMeasures · Answer

1% is quite small and hence even simple interest calculation with it'll yield result quite close to comp interest. So ans A

Nina1987 · Answer

But how far can we assume SI=CI? 1%? 2%? 3%?

GMATinsight · Answer

Let population in the beginning = 100
at the end of 1st year population = 100+1% of 100 = 100+1 = 101
at the end of 2nd year population = 101+1% of 101 = 101+1 approx = 102 approx (on the lower side because 1% of 101 is greater than 1)
at the end of 3rd year population = 102+1% of 102 = 102+1 approx = 103 approx (on the lower side because 1% of 102 is greater than 1)
at the end of 4th year population = 103+1% of 103 = 103+1 approx = 104 approx (on the lower side because 1% of 103 is greater than 1)
at the end of 5th year population = 104+1% of 104 = 104+1 approx = 105 approx (on the lower side because 1% of 104 is greater than 1)

i.e. 5% greater than 25000 = 25000+5% of 25000 = 25000+1250 = 26250 (on the lower side)

i.e. Population must be greater than 26250 but since the closest option is 26000 so

Answer: option A

ScottTargetTestPrep · Answer

After 1 year, the population will be:

25,000 + 250 = 25,250

After 2 years, the population will be:

25,250 + 252 = 25,502

After 3 years, the population will be:

25,502 + 255 = 25,757

So essentially, we see that the population growth is a little more than 250 people a year.

25,000 + 250 x 5 = 26,250, so about 26,000.

Alternate solution:

The population of the town in 5 years is:

25,000 x (1 + 0.01)^5 = 25,000 x 1.01^5 = 26,275, which is closest to 26,000.

Answer: A

Basshead · Answer

1% of 25,000 = 250

Since 1% compounded is really insignificant, we can use simple interest:  250 * 5 = 1,250

25,000 + 12,250 = 16,250

Closest answer is A.

harish555 · Answer

We can use Simple Interest formula - SI = PTR/100. Here , P = 25000, T=5, R=1 . therefore, PTR/100 = 1250. Therefore, the population of the town after 5 years would be closest to 26000. (25000+1250* = 26000*)

BongBideshini · Answer

We can solve this question using Binomial Expansion Formula
 (1+x)^n= 1 + n x +   x^2 +   x^3 +...
In this question, x=1/100, which is a very small number. So, we can avoid higher order terms (x^2, x^3,....)
So,
25000(1+1/100)^5=25000(1+5/100)
 =25000+25000*5/100
 =25000+1250
 =26250 Ans(A)

bumpbot · Answer

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If a town of 25,000 people is growing at a rate of approximately 1

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