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?
\(A = P(1 + \frac{R}{100})^{T}\)
\(285.20 = P(1 + \frac{5}{100})^{3}\)
\(285.20 = P(1.05)^{3} \implies 1.16P = 285.20\)
\(P = \frac{285.20}{1.16} = $245.86\)
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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