Question

You expect to have $ 6,000 in one year. A bank is offering loans at 5.0 % interest per year. How much can you borrow​ today?

Today you can borrow ​$           . ​(Round to the nearest​ cent.)

You are thinking of building a new machine that will save you $ 1,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 1 % per year forever. What is the present value of the savings if the interest rate is 9 % per​ year?

The present value of the savings is ​$          . ​(Round to the nearest​ dollar.)

You are thinking of purchasing a house. The house costs $ 350,000. You have $ 50,000 in cash that you can use as a down payment on the​ house, but you need to borrow the rest of the purchase price. The bank is offering a 30​-year mortgage that requires annual payments and has an interest rate of 6 % per year. What will be your annual payment if you sign this​ mortgage?

The annual payment is ​$              ​(Round to the nearest​ dollar.)

Answer 1

1.Present value=$6000*Present value of discounting factor(rate%,time period)

=$6000/1.05

=$5714.29(Approx).

2.Present value=Savings for 1st year/(Interest rate-Growth rate)

=1000/(0.09-(0.01))

=1000/0.1

=$10,000

3.

Total borrowings to be made=(350,000-50,000)=$300,000

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

300,000=Annuity[1-(1.06)^-30]/0.06

300,000=Annuity*13.76483115

Annuity=300,000/13.76483115

=$21795(Approx).