bond whose value grew

[sanju09]

Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 6.25%
(B) 6.67%
(C) 8.33%
(D) 12%
(E) 12.5%

[Anurag@Gurome]

Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 6.25%
(B) 6.67%
(C) 8.33%
(D) 12%
(E) 12.5%

Let the initial sum of money invested = $P, Rate = R, and Time = T
Amount at the end of 3 years = $300 = P(1 + 3R/100)
Amount at the end of (3 + 5 =)8 years = $400 = P(1 + 8R/100)
Dividing the 2 equations, we get,
[1 + 3R/100]/[1 + 8R/100] = 3/4
4 + 12R/100 = 3 + 24R/100 or 1 = 12R/100
R = 100/12 = 25/3 = 8.33%

The correct answer is C.

[vineeshp]

C?

100 increase in 5 years, so per year is 20.

300 at the end of 3 years (increase of 3 * 20) -> 240 at the beginning.

So interest paid out 20/240 * 100 gives 8.33

[force5]

8.33 same way