A sum of money invested at 5% per annum simple interest amounts to $285.20 after 3 years. How long will it take the same sum to amount to $434.00 at 7(frac{1}{2})% per annum simple interest?

A.
7(frac{1}{2}) years 
B.
10 years 
C.
5 years 
D.
12 years 
E.
14 years
Correct Answer: Option B
Explanation
(A = P(1 + frac{R}{100})^{T})
(285.20 = P(1 + frac{5}{100})^{3})
(285.20 = P(1.05)^{3} implies 1.16P = 285.20)
(P = frac{285.20}{1.16} = $245.86)
Given Amount = $434.00
Interest = Amount – Principal
Interest = $434.00 – $245.86 = $188.14
(T = frac{100I}{PR})
(T = frac{100 times 188.14}{245.86 times 7.5})
(T = frac{18814}{1843.95} = 10.2)
Approximately 10 years.