The following questions relate to financial security S$,$ which operates as follows: A price

P is paid $($by the investor$)$ in return for a series of interest payments of D payable at the

end of each of the next n years, and a final redemption payment of R payable at the end

of the n years. The investor earns an annual effective rate of return of i$.$

$($a$)$ Calculate P$,$ given that D $=5,$ R $=125,$ i $=10\%$ and n $=20.$

$($b$)$ Calculate n$,$ given that P $=83\mathrm{.}73,$ D $=4,$ R $=101$ and i $=6\%.$

$($c$)$ Calculate i$,$ given that P $=75,$ D $=5,$ R $=120$ and n $=10.$