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
