simple interest rate

[datonman]

A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

1.) 6%
2.) 6.5%
3.) 7.5%
4.) 8%

[Brent@GMATPrepNow]

A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

1.) 6%
2.) 6.5%
3.) 7.5%
4.) 8%

With simple interest, one's investment increases the SAME AMOUNT each year, based on the INITIAL investment.

$18,400 - $16,000 = $2400
So, the investment increased $2400 over 2 YEARS
$2400 ÷ 2 = $1200
So, the ANNUAL increase is $1200

The INITIAL INVESTMENT was $16,000
$1200/$16,000 = [spoiler]7.5%[/spoiler]

Cheers,
Brent

[datonman]

This looks very helpful. Thank you. The one method I tried to do. Emphasis on the word 'tried,' is that i was trying to use the formula.

A=P +I or Amount = Principal + Interest

I tried to use A = P(1+RT/100) and just plug in the info from the question. I wonder what I did wrong.

[[email protected]]

Hi datonman,

The two interest rate formulas that the GMAT could test you on are:

1) Simple Interest: Principal x (1 +rt)

2) Compound Interest: Principal x (1 + r)^t

In both formulas....

"Principal" represents the initial investment
"r" represents the interest rate, as a decimal
"t" represents the number of years

Given the information in this question, we'd use the Simple Interest Formula and plug in the values that we're given:

16,000 x (1 + r(2)) = 18,400

(1 + 2r) = 18,400/16,000

(1 + 2r) = 184/160

(1 + 2r) = 23/20

(1 + 2r) = 1.15

2r = 0.15

r = .075

Final Answer: [spoiler]7.5% or answer #3[/spoiler]

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

1.) 6%
2.) 6.5%
3.) 7.5%
4.) 8%

With simple interest, one's investment increases the SAME AMOUNT each year, based on the INITIAL investment.

$18,400 - $16,000 = $2400
So, the investment increased $2400 over 2 YEARS
$2400 ÷ 2 = $1200
So, the ANNUAL increase is $1200

The INITIAL INVESTMENT was $16,000
$1200/$16,000 = 7.5%

Cheers,
Brent

[Jeff@TargetTestPrep]

A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

1.) 6%
2.) 6.5%
3.) 7.5%
4.) 8%

The amount of interest earned is 2,400. Using the formula for simple interest I = P x r x t, where I = interest, P = principal, r = rate, and t = time, we have:
2400 = 16,000 x r/100 x 2

2400 = r/100 x 32,000

240,000 = r x 32,000

r = 240,000/32,000 = 240/32 = 30/4 = 7.5

Answer: C

[mbawisdom]

A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

1.) 6%
2.) 6.5%
3.) 7.5%
4.) 8%

18,400 = 16,000(1 + R.2)
18,400 = 16,000 + 32,000.R
2,400 = 32,000.R
R = 2,400/32,000
R = 0.075
R = 7.5%

Alternatively:

Interest over 2 years = 18,400 - 16,000 = 2,400
Interest over 1 year = 2,400/2 = 1,200
Rate = 1,200/16,000
Rate = 7.5%