Consider the annuity formula with positive payments, C $>0.$ The present value of the annuity is

A$.$ Decreasing in the interest rate and increasing in the number of payments

B$.$

Increasing in the interest rate and decreasing in the number of payments

C$.$ Increasing in the interest rate and increasing in the number of payments

D$.$

Decreasing in the interest rate and decreasing in the number of pavments

Consider a growing annuity with positive payoffs. The present value of the growing annuity is

A$.$ Increasing in the growth rate and increasing in the number of payments

B$.$ Decreasing in the growth rate and increasing in the number of payments

C$.$ Increasing in the growth rate and decreasing in the number of payments

D$.$ Decreasing in the growth rate and decreasing in the number of payments

You are considering two investments. The US Treasury offers the first investment: it pays $$1000$ per year forever. An Al firm offers the second investment. It pays $$800$ next year but is expected to grow at $8\%$ forever. Suppose that

the risk$-$free rate is $2\%.$ but the Al firm's cost of capital is $10\%.$ Which investment do you select?

A$.$ The Al Firm: We must submit to our robotic overlords

B$.$ It does not matter: both have infinite value because they pay forever

C$.$ The Al Firm: Because it grows at $8\%,$ it will be much more than the Ireasury

$$ D$.$ The Treasury: It has a higher present value

You own a nuclear power plant. Though it is a carbon neutral source of energy, you have spent nuclear fuel $($nuclear waste$)$ to clean up$.$ You can store it safely, or you can pay a one$-$time fee to a clean$-$up firm to dispose of it$.$ Sate

storage will require paying sTUU a year torever. Ine clean$-$up specialists will charge $$1900$ to remove the waste. If your cost of capital is $5\%,$ should you outsource to the specialists or do it yourselt?

A$.$ Outsource to the clean$-$up specialists

B$.$ Store the nuclear waste

When you solve a finance problem, what is the first step?

A$.$ Write a Timeline of Cashflows

B$.$ Drink Coffee

C$.$ Buy Rising Roll

D$.$ Clean your room