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  3. the force of interest varies as a linear function

The force of interest varies as a linear function from t = 0 until t =...

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Advance Math

The force of interest varies as a linear function from t = 0until t = 5 and as a quadratic function From t = 5 until t =10 (tin years) and is continuous at all time points.

Suppose the force of interest is 2% p.a. at t = 0, 4.5% p.a. att =5, 8% p.a. at t = 8 and 10% p.a. at t = 10.

a) Determine the functional form of the force of interest overthe 10 year period

b) A company receives a cash-flow from t=1 until t=5 at the rateof (100+25t) per unit time.

The company pays out a cash flow from t = 6 until t = 8 at therate of (-t^2 +48t - 80 )per unit time.  Calculate thenet present value of the company’s cash flow position at t = 0

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