A UK household is considering whether to invest the sum of £7000 on a renewable energy system, which generates 3.5 MWh of energy per year for 15 years, or to invest the money in a bank at 1.25% interest rate compounded annually for the same period. A technology vendor has informed the household that the current UK Feed-in-Tariff for this technology is 4.5p per kWh generated, plus 16p per kWh gained through reduced energy bills.
(i) Estimate the payback period for the renewable energy system, to the nearest whole number of years.
(ii) Estimate the net income that can be generated from the renewable energy system over its 15-year lifetime.
(iii) Calculate the gross income that can be obtained, if the money is deposited in the bank at the given compound interest rate for 15 years.