In: Advanced Math
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
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 |