144144 wrote:
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 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 #1We 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 E, which can be written as (8/3)d, is BETWEEN
2d dollars and
3d So, the correct answer must be E
APPROACH #2To 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