The interest ($/) received from an investment varies jointly as the interest rate per annum (%) and the period of investment (T years). If a sum of money is invested for 2 years at an interest rate of 8% p.a., the interest received will be $800. (a) Express I in terms of r and T. (b) If the same sum of money is invested for 3 years at an interest rate of 14% p.a., find the interest received.
Question
The interest (800. (a) Express I in terms of r and T. (b) If the same sum of money is invested for 3 years at an interest rate of 14% p.a., find the interest received.
Solution
(a) The problem states that the interest (I) varies jointly as the interest rate (r) and the period of investment (T). This can be expressed as I = krT, where k is the constant of variation.
To find the value of k, we can use the information given in the problem: when r = 8% (or 0.08 as a decimal) and T = 2 years, I = $800. Substituting these values into the equation gives 800 = k0.082. Solving for k gives k = 800 / (0.08*2) = 5000.
So, the equation relating I, r, and T is I = 5000rT.
(b) To find the interest received when the same sum of money is invested for 3 years at an interest rate of 14% p.a., we can substitute r = 14% (or 0.14 as a decimal) and T = 3 years into the equation. This gives I = 50000.143 = $2100.
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