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

Colby Messinger answered 1 year ago

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