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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 (/)receivedfromaninvestmentvariesjointlyastheinterestrateperannum(/) 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.

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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.

This problem has been solved

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