(a) Suppose you deposit $1,000 into a savings account that earns interest at the rate of 6% per annum, compounded semi-annually. What would be the balance in the account:

(i) after six years?

(ii) after 20 years? (3 marks)

(b) Ted wants to borrow from Fred. Ted is confident that he will have $1,000 available to pay off Fred in two years. How much will Fred be willing to lend to Ted in return for $1,000 two years from now if he uses annual interest rates (compounded quarterly) of :

(i) 5%?

(ii) 15%? (3 marks)

(c) How long will it take for an amount of $1,000 to double if interest is paid at 10 percent per annum if:

(i) compounded semi-annually? (2 marks)

(ii) compounded quarterly? (2 marks)