# Paul fell off his bike and damaged his neck. Without treatment his health-related quality of life…

Paul fell off his bike and damaged his neck. Without treatment his health-related quality of life (HRQoL) is expected to be 0.75 for the rest of his life. Paul is expected to live for another 50 years regardless of which of the following two treatments he receives.

*Neck surgery*: Costs $16,000 immediately and increases Paul’s HRQoL to 1.0 for the rest of his life, but requires annual checkups costing $300 each (paid at the end of each year).

*Physiotherapy*: Costs $1000 per year (paid at the end of each year) and increases Paul’s HRQoL to 0.95 for the rest of his life. In 10 years’ time he will also need a minor procedure costing 00 (paid at the end of that year).

For the following questions, assume a discount rate (*r*) of 5% per annum and note that the present value of an annuity of *a* per annum for *n* years at *r* rate of discount is given by the formula:

– (or, equivalently, *a*[– ])

What is the present value of the cost of *Neck surgery*?

What is the present value of the cost of *Physiotherapy*?

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