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
