Suppose we enter into a complex financial arrangement in which I pay you $$50$ next year, $$100$ in two years year and $$200$ in $3$ years. You will earn an interest rate of $10\%.$

Draw a cash flow timeline to express this arrangement. $(2$ points$)$

How much would you pay today for this arrangement? $(13$ points$)$

What is the APR on a $10-$year annuity that makes $$100$ quarterly payments and costs $$10,000$ today? $(10$ points$)$

What would you pay today for a perpetuity due that offers $10\%$ EAR and a $2\%$ annual growth rate? The perpetuity paid $$2$ this month? $(35$ points$)$

HINT: This is a multi$-$part problem. Figure out what the periodic rate is$,$ then use it to value the perpetuity due.

BONUS: Suppose I buy a pet tiger for $$10,000.$ Every month I have to feed him $$1000$ worth of vegetarian tiger food. I get tired of this after two years and sell him for $$5000.$ What was my return on investment? $(15$ points$)$