$7.$ Orlando has decided to open a bookstore$/$caf$$ and needs to borrow from his sister. In exchange for a lump

sum today, he offers to pay her $$3500$ in one year's time, $$4500$ in two years' time, $$5000$ in three years' time

and another $$5000$ in $4$ years' time. If the interest rate is $7\%,$ what is the lump sum Orlando can expect to

receive from his sister if the net present value $($NPV$)$ is to be equal to zero? $($That is$,$ if his sister should not

make a loss.$)$ Show your work. Draw a timeline.