Janet seeks to give her niece Rita $6,000 for her college

Question

Janet seeks to give her niece Rita $6,000 for her college education on the day she attends her first lecture. A special education account through her bank offers a rate of 20% interest compounded annually on a deposit of $1,000. Approximately how many years before her niece is due to begin college should Janet make such a deposit?

 (A) 8 (B) 9 (C) 10 (D) 11 (E) 12

shoonya · Answer

guys, i know it will be a lengthy calculation.

any easy way to answer this?

jainvik7 · Answer

More than 9 years.

So the answer is 10 years. Option C.

Whats the OA ?

shoonya · Answer

it should be more than 9 years. so 10 years is the minimum.

(1.2)^n > 6

6 can be broken down as

1.2*1.2*1.2*.....1.2

eq is satisfied for any n more than 9.

rnachloo · Answer

Ok, this is what I did. It took me more than 2 minutes, but I was able to get the answer in a reasonable time. 

we had to calculate 1.2 to the power n.

I took it as 
12 * 12 = 144 ~= 14
14 * 12 = 178 ~= 17
17 * 12 = 170 + ~34 = 204 ~= 20
20 * 12 = 240 ~= 24
24 * 12 = 240 + 48 ~= 288 ~= 28
28 * 12 = 280 + 56 ~= 336 ~= 33
33 * 12 = 330 + 66 ~= 396 ~= 39
39 * 12 = 390 + 78 ~= 468 ~= 46
46 * 12 = 460 + 92 = 552 ~= 55
55 * 12 = 550 + 110 = 660 ~= 66 (above 6)

Total is 10 years. I actually calcuated majority of this in mind, hence was able to complete it in less than 3 minutes or so. It would be very difficult to do this if you have a bigger number like 27 or 17 or something. Don't know any other efficient number. I showed this way to you so that if the number is small sometimes we could use brute force to calculate the value.

If anyone knows of a better method, please let me know.

kevincan · Answer

According to your work, your answer should have been 11 years, not 10. Be careful, though. You're always rounding down. Why not alternate so as to lessen the bias? Can somebody come up with a better method to get the correct answer, which is indeed 10 years? Your two mistakes cancelled each other out!

rnachloo · Answer

Ok, this is what I did. It took me more than 2 minutes, but I was able to get the answer in a reasonable time. 

we had to calculate 1.2 to the power n.

I took it as 
12 * 12 = 144 ~= 14
14 * 12 = 178 ~= 17
17 * 12 = 170 + ~34 = 204 ~= 20
20 * 12 = 240 ~= 24
24 * 12 = 240 + 48 ~= 288 ~= 28
28 * 12 = 280 + 56 ~= 336 ~= 33
33 * 12 = 330 + 66 ~= 396 ~= 39
39 * 12 = 390 + 78 ~= 468 ~= 46
46 * 12 = 460 + 92 = 552 ~= 55
55 * 12 = 550 + 110 = 660 ~= 66 (above 6)

Total is 10 years. I actually calcuated majority of this in mind, hence was able to complete it in less than 3 minutes or so. It would be very difficult to do this if you have a bigger number like 27 or 17 or something. Don't know any other efficient number. I showed this way to you so that if the number is small sometimes we could use brute force to calculate the value.

If anyone knows of a better method, please let me know.

jaynayak · Answer

6000 = 1000 (12/10) ^n

(1.2)^n = 6

Hence n ~ 10
Lengthy calculation . still trying to find a shorter way.

BG · Answer

The last step can be eliminated since once the initial investment has increased five times, with rate of increase 20% on the next year it will be 6

kevincan · Answer

Hint: sqrt (2) a a little more than 1.4!

We need 1.2^n =6 (approx)

1.2^2 =1.44
so 1.2^4 is just over 2
1.2^8 is just over 4
1.2^10=1.2^8*1.2^2 will be very close to 6

or 1.2^3 is about 1.73 which is close to sqrt(3)
so 1.2^9 is about 3*sqrt(3), just over 5
so 1.2^10 will be just over 6

Janet seeks to give her niece Rita $6,000 for her college

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