We now turn to a financial asset called a bond. It is a security issued by a government or a corporation to finance their operations. Against payment by the lender of an amount P $ upfront, the borrower commits on reimbursing at the end of year $n$ an amount of $1$$$,$ and at the end of each intermediate year $($including last year$)$ an amount $c$$ :

$1+c$

$c$ is a fraction of the nominal amount $(1S$ in the above case$),$ for instance $c=4\%.$ This amount is therefore paid each year to make the lender $"$ bear with $"$ the borrower until the end. Thus, if $c=0,$ against payment of a sum $P$ by the lender, the borrower must pay back I in $n$ years, but nothing in between. While such bond is a means for the borrower to finance his venture, it is at the same time an investment asset for the lender who can thus invest his money during the whole life of the loan thus granted.

Compute and simplify the formula giving $P$ by expressing the fact that this quantity is equal to the sum of the present values of the flows of each year $(1,2,3,$dotsn$).$