Here are a few problems on present values. In all of the following examples, assume that you can both borrow and lend at annual interest rate of r and that the interest rate will remain the same forever.

(a) You would be indifferent between getting $1 now and _______ dollars, one year from now, because if you put the dollar in the bank, then one year from now you could get back _________ dollars from the bank. 

(b) You would be indifferent between getting _____dollar(s) one year from now and getting $1/(1+r) dollars now, because  _________ deposited in the bank right now would enable you to withdraw principal and interest worth $1.

(c) For any X > 0, you would be indifferent between getting _________ dollars right now and $X one year from now. The present value of $X received one year from now is ____________ dollars.

(d) The present value of an obligation to pay $X one year from now is __________ dollars.

(e) The present value of $X, to be received 2 years from now, is __________ dollars.

(f) The present value of an asset that pays X_t dollars t years from now is _______ dollars.

(g) The present value of an asset that pays $X₁ one year from now, $X₂ in two years, and $X₁₀ ten years from now is _______________________ dollars.

(h) The present value of an asset that pays a constant amount, $X_per year forever can be computed in two different ways. One way is to figure out the amount of money you need in the bank so that the bank would give you $X per year, forever, without ever exhausting your principal.

The annual interest received on a bank account of ___________ dollars will be $X. Therefore having ________ dollars right now is just as good as getting $X a year forever.

(i) Another way to calculate the present value of $X a year forever is to evaluate the infinite series _________ . This series is known as a __________ series. Whenever r > 0, this sum is well defined and is equal to ___________.

(j) If the interest rate is 10%, the present value of receiving $1,000 one year from now will be, to the nearest dollar, ______. The present value of receiving $1,000 a year forever, will be, to the nearest dollar,___________.

(k) If the interest rate is 10%, what is the present value of an asset that requires you to pay out $550 one year from now and will pay you back $1,210 two years from now __________________ dollars?