"An investment of d dollars at k percent simple annual interest yields $600 over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
(A) 2d/3
(B) 3d/4
(C) 4d/3
(D) 3d/2
(E) 8d/3
An investment of d dollars at k percent simple annual interest yields $600 over a 2-year period.
In other words, an investment of d dollars yields $300 in interest
each year.
What dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
In other words, how much money must we invest to earn
$800 in interest
EACH YEAR?
If a
d dollar investment yields
$300 in interest EACH YEAR, then:
- a
2d dollar investment would yield
$600 (2 times $300) in interest EACH YEAR
- a
3d dollar investment would yield
$900 (3 times $300) in interest EACH YEAR
- a
4d dollar investment would yield $
1200 (4 times $300) in interest EACH YEAR
- etc.
From here there are two approaches.
APPROACH #1
We want the ANNUAL interest to be
$800.
This means we must invest an amount that is BETWEEN
2d dollars and
3d dollars
[since $800 is BETWEEN $600 and $900].
When we check the answer choices, only [spoiler]E, which can be written as (8/3)d,[/spoiler] is BETWEEN
2d dollars and
3d
So, the correct answer must be
E
APPROACH #2
To increase the ANNUAL interest from
$300 to
$800, we must invest
800/
300 TIMES as much money.
800/300 = 8/3, so we must invest (8/3)d dollars
[aka 8d/3 dollars]
Answer =
E
Cheers,
Brent
