# (i) You are thinking of building a new machine that will save you \$4000 in the first year. The…

(i) You are thinking of building a new machine that will
save you \$4000 in the first year. The machine will then begin to wear out so
that the savings decline at a rate of 4% per year forever. What is the present
value of the savings if the interest rate is 10% per year?

(ii) A rich aunt has promised you \$2000 one year from today.
In addition, each year after that, she has promised you a payment (on the
anniversary of the last payment) that is 7% larger than the last payment. She
will continue to show this generosity for 20 years, giving a total of 20
payments. If the interest rate is 7%,

(i) You are thinking of building a new machine that will
save you \$4000 in the first year. The machine will then begin to wear out so
that the savings decline at a rate of 4% per year forever. What is the present
value of the savings if the interest rate is 10% per year?

(ii) A rich aunt has promised you \$2000 one year from today.
In addition, each year after that, she has promised you a payment (on the
anniversary of the last payment) that is 7% larger than the last payment. She
will continue to show this generosity for 20 years, giving a total of 20
payments. If the interest rate is 7%, what is her promise worth today?

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