A project is to build a windmill. It will cost $£1,000,000$ to build and it will generate income (after costs) of $£80,000$ per year, paid annually for fifty years, with the first payment made in 2 years’ time. Bank finance is available at the rate of 6% (annual effective rate). Show that the yield is approximately $7.2\%$.
What should this bank finance mean? If we ignored it (as the question has a lot of parts, so I thought I might not need it now), we would consider
$$ 0 = -1000000 + 80000\sum_{k=2}^{51}v^k = -10^6 + 8\times 10^4 \times \frac{v^{52}-v^2}{v-1}$$
But in this case $i = 7.2%$ (i.e. $v \sim 0.993$ is quite far from the solution of the above equation.
Any help appreciated!