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Compound interest

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by Cheese12 » Sun Oct 02, 2011 12:30 am
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
A) 16 = (1.02)x/4
B) 2 = (1.02)x
C) 16 = (1.08)4x
D) 2 = (1.02)x/4
E) 1/16 = (1.02)4x

Hi all, could you pls tell me a another way to solve this problem other than using the formula.. pluggin in takes a long time.. is there another quicker method to do this one ?

Thanks!!





OA: B
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by GMATGuruNY » Sun Oct 02, 2011 2:56 am
Cheese12 wrote:A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?

A) 16 = (1.02)^x/4
B) 2 = (1.02)^x
C) 16 = (1.08)^4x
D) 2 = (1.02)^x/4
E) 1/16 = (1.02)^4x
When a value increases repeatedly by r%:

Final amount = Original amount * (1 + r/100)^number of changes.

Let original amount = 1.
Since the original amount increases by a factor of 16:
Final amount = 16.
Since the investment increases by 2% every quarter:
r = 2.
Since x = the number of years, and there are 4 changes every year:
Number of changes = 4x.

Plugging these values into the formula:

16 = 1*(1.02)^4x
16^(1/4) = 1.02^(4x*(1/4))
2 = 1.02^x

The correct answer is B.
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by rohit_gmat » Sun Oct 02, 2011 3:12 am
GMATGuruNY wrote:
Cheese12 wrote:A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?

A) 16 = (1.02)^x/4
B) 2 = (1.02)^x
C) 16 = (1.08)^4x
D) 2 = (1.02)^x/4
E) 1/16 = (1.02)^4x
When a value increases repeatedly by r%:

Final amount = Original amount * (1 + r/100)^number of changes.

Let original amount = 1.
Since the original amount increases by a factor of 16:
Final amount = 16.
Since the investment increases by 2% every quarter:
r = 2.
Since x = the number of years, and there are 4 changes every year:
Number of changes = 4x.

Plugging these values into the formula:

16 = 1*(1.02)^4x
16^(1/4) = 1.02^(4x*(1/4))
2 = 1.02^x

The correct answer is B.
Hi! thanks for your reply...

Please correct my understanding for this part...
"annual interest rate of 8%, compounded quarterly" I thought this meant that the amount is increased by 8% in each quarter of an year...

"compounded quarterly"... means that the percent increase is added every quarter right ? Am I missing out on something ?

Thanks a lot for your help !! :)
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by sl750 » Sun Oct 02, 2011 3:22 am
The principle plus interest in this case is compounded 4 times in a year, that is what it means
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by GMATGuruNY » Sun Oct 02, 2011 3:23 am
rohit_gmat wrote:
GMATGuruNY wrote:
Cheese12 wrote:A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?

A) 16 = (1.02)^x/4
B) 2 = (1.02)^x
C) 16 = (1.08)^4x
D) 2 = (1.02)^x/4
E) 1/16 = (1.02)^4x
When a value increases repeatedly by r%:

Final amount = Original amount * (1 + r/100)^number of changes.

Let original amount = 1.
Since the original amount increases by a factor of 16:
Final amount = 16.
Since the investment increases by 2% every quarter:
r = 2.
Since x = the number of years, and there are 4 changes every year:
Number of changes = 4x.

Plugging these values into the formula:

16 = 1*(1.02)^4x
16^(1/4) = 1.02^(4x*(1/4))
2 = 1.02^x

The correct answer is B.
Hi! thanks for your reply...

Please correct my understanding for this part...
"annual interest rate of 8%, compounded quarterly" I thought this meant that the amount is increased by 8% in each quarter of an year...

"compounded quarterly"... means that the percent increase is added every quarter right ? Am I missing out on something ?

Thanks a lot for your help !! :)
An annual rate of 8%, compounded quarterly means that 1/4 of the annual interest rate is received every quarter:
Interest rate per quarter = (1/4)*8 = 2%.

Let the initial investment = 10,000.
Amount after the first quarter = (1.02)*10,000 = 10,200.
Now we receive 2% of the NEW amount.
Amount after the second quarter = (1.02)*10,200 = 10,404.
etc.
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