BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Can we use the PRT/100 formula here?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Sun Mar 15, 2015 7:27 am
Thanked: 2 times
Followed by:1 members

Can we use the PRT/100 formula here?

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
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sun Mar 15, 2015 9:22 pm

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.
Top
Post new topic Post Reply
• Page 1 of 1