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Can we use the PRT/100 formula here?

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by src_saurav » Sat Apr 04, 2015 11:29 pm
In 16 years, an investment earning x% simple annual interest triples in value. How many years does it take the investment to double in value?

A)7 years
B)8 years
C)8.5 years
D)9 years

My solution

300=100*R*16
r=3/16


200=100*3/16*T


I am not getting the right answer...

What is your answer
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by GMATGuruNY » Sun Apr 05, 2015 2:54 am
In 16 years, an investment earning x% simple annual interest triples in value. How many years does it take the investment to double in value?

A)7 years
B)8 years
C)8.5 years
D)9 years
Since the investment takes 16 years to triple in value, it takes 16 years to earn 200% in interest.
We must determine how many years are required for the investment to earn 100% in interest, with the result that the investment doubles in value.
Set up the following proportion:

(200 percent)/(16 years) = (100 percent)/(x years)
200x = 1600
x = 8 years.

The correct answer is B.
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by Brent@GMATPrepNow » Sun Apr 05, 2015 7:32 am
src_saurav wrote:In 16 years, an investment earning x% simple annual interest triples in value. How many years does it take the investment to double in value?

A)7 years
B)8 years
C)8.5 years
D)9 years
Mitch's approach is the best (i.e., fastest) approach here.
However, if you didn't spot that approach, you can also use some algebra.

Let's say that we start with an initial investment of $100, and after 16 years, the investment is worth $300 (it triples).
Since the SIMPLE INTEREST rate is x%, we earn x% of $100 EACH YEAR.
x% of $100 = x, so the interest is x dollars each year.

So, here's what we have:
Year 0: $100
After 1 year: 100 + x
After 2 years: 100 + x + x
After 3 years: 100 + x + x + x
After 4 years: 100 + 4x
.
.
.
After 16 years: 100 + 16x
We know that 100 + 16x = 300
So, 16x = 200
Solve: x = 12.5
So, the simple interest rate is 12.5%
This means that the investment earns interest of $12.50 EVERY YEAR

How many years does it take the investment to double in value?
So, how many years for the investment to go from $100 to $200?
At an increase of $12.50 each year, the number of years for the investment to increase $100 will equal $100/$12.50 = 8

The correct answer is B.

Cheers,
Brent
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by [email protected] » Wed Apr 08, 2015 1:41 am
Hi Saurav,

You initial equation 300 = 100*R*16 is wrong. The questions says that the investment is tripled in 16 years.

You had not added the initial principal amount in this equation.

What your equation says is that the final interest amount is 3 times the initial principal amount.

You need to write equation in this form:

Final Investment(F.I.) = Initial Investment(I.I.) + Simple Interest(S.I.)

If I.I. = 100, then F.I.=300

=> 300 = 100 + (100*R*16)
=> R=12.5%

Now, I.I. = 100 and F.I.=200, then T=?

=> 200 = 100 +((100*12.5*T)/100)
=> T = 100/12.5 = 8 years


Please see that Mitch's approach is fastest here.
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