Home » A sum of money invested at 5% per annum simple interest amounts to $285.20 after…

A sum of money invested at 5% per annum simple interest amounts to $285.20 after…

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.