Question

In: Advanced Math

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

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

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

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

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

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

Solutions

Expert Solution

Please see the below images and table for step by step computation for both sub-parts of the question:

t Cash Flow, C(t) Rate Computation Present Value
1 125 2.5 125/(2.5)^1 50
2 150 3 150/(3)^2 16.66667
3 175 3.5 175/(3.5)^3 4.08163
4 200 4 200/(4)^4 0.78125
5 225 4.5 225/(4.5)^5 0.12193
6 -172 5.73 (-172)/(5.73)^6 -0.00486
7 -207 6.9 (-207)/(6.9)^7 -0.00028
8 -240 8 (-240)/(8)^8 -0.00001
NPV: 71.64633

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