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 is B

$A = P(1 + \frac{R}{100})^{T}$

$285.20 = P(1 + \frac{5}{100})^{3}$

$285.20 = P(1.05)^{3} \implies 1.16P = 285.20$

$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.

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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?