Answer the following questions

(a)Rowan has invented a new household device that would earn him $12,000 per annum for the next 10 years. Given an interest rate of 10% compounded annually, would Rowan be willing to sell his invention today for $100,000?

(b) Kate won a lottery that will make a payment $100,000 every year, starting today, for the next 10 years. If she invests the payments at a rate of 4.00% per year, what is the present value of the cash flows over the 10 year period? Interest for the 10 equal payments will be compounded at the end of each year.

(c) Property Trust Bank pays its clients 8% interest per annum, compounded on a semi-annual basis. To remain competitive, the bank's major competitor, Mortgage Trust Bank is willing to match the interest rate offered by Property Trust Bank, but interest will be compounded on a quarterly basis. What nominal rate of interest must Mortgage Trust Bank offer to its clients?