Question

1. A black box spews out $100 today and then every year, forever. The risk-free rate is currently 7% per year, and is not expected to change. What is the value of the black box today, before the first $100 are spewed out? 2. What is the value of the box from Q1, if the amount it spews out grows by 5% every year (i.e., it'll be $105 in 1 year, $110.25 in two years, ...)? 3. What is the value of the box from Q2, if we now learn that it'll stop spewing money in 10 years (after spewing out its 11th payment)? 4. You are now told that the box from Q2 will stop spewing money in M years. You are also told this box is traded for $3000 today. What is the market's estimate of M (round to nearest year)? 5. The box from Q3 was upgraded to spew out $A today, still grows by 5% per year and stops in 10 years. You are given that it is worth $4000. What is A? 6. Money moves from time to to time T1 with rate 0.08, from T1 to T2 at rate 0.09, and from TO to T3 at rate 0.25. What is the rate by which money moves from T2 to T3? 7. You lend $100 to a stranger for two years, at 10% yearly interest (APR), but you agree that interest will be compounded every month. How much does the stranger owe you after two years?

Answer 1

1.

The value of black box is calculated below:

Cash flow Present value = Cash flow + Interest rate

100 Present value = 100+ 0,07

Present value = 100 + 1, 428.57

Present value = 1,528.57