A new renewable energy generation system has a life-time of 10 years. It is assumed that the salvage value of the system at the end of the 10 years' life-time is negligible. The initial (Present time) investment of the system costs 50,000 HK$. The manufacturer agrees to maintain the system every year over the 10 years' life-time with a uniform annual maintenance fee of 1000 HK$/year. At the end of the 5th year, a key component should be replaced, which will cost 10,000 HK$. Each year, this renewable energy system will generate 5,000 kWh electricity. It is assumed that the electricity price in the first year is 1 HK$/kWh, with an annual escalation rate of 3%. The interest rate is 5%.

Please calculate:

(1) The present value of the total maintenance fee over 10 years' life-time.

(2) The present value of the total saved electricity cost over 10 years' life-time.

(3) The net present value of this system, by considering all the cash flows mentioned in the question statement.

(4) If the replacement cost 10,000 HK$ of the key component at the end of the 5th year is accumulated by depositing a fixed amount of money per year in the first 5 years, how much should be this deposited money per year?

(5) Based on the above questions , please investigate that how the "interest rate" and its variation will affect the results of the above questions, and discuss and comment on their sensitivity. For example, the "interest rate" varies +/- 0~0.03 based on the original 0.05 (i.e. the interest rate varies in the range between 2%~8%).(*two page report is required)