Planning for the future $(15$ points$)$

a$)$ Marie won the lottery and wants to use some of her winnings to start a fund to provide her

aging parents with $$25,000$ per year for $20$ years. The fund has an annual return of $8\%.$ How

much should she put in the fund to support her parents? Show your work.

b$)$ Marie is also considering adding an accessory dwelling unit $($ADU$)$ to her home in downtown

Burlington. The unit would cost $$80,000$ to build, which she would finance with a loan with

$5\%$ interest. She is hoping to recover her investment within $7$ years when her kids go to

college, so that the rental income at that time can contribute to their tuition costs. How

much rent would the ADU need to earn to pay back her initial investment within $7$ years?

Show your work.

c$)$ Describe two external effects $($costs or benefits$)$ of building an ADU. Indicate whether each

is a cost or a benefit.