1. Alice wishes to purchase an annuity which will pay her $1600 at the end of each three months for 8 years. The rate of interest is 6% compounded quarterly. The premium she will pay today for the annuity is equal to the present value of the cash flow. Find the present value of this cash flow. 2. Joel has set up a savings account to make a down payment on a new car. He will deposit $280 at the end ofeach monuh for five years into a savings account. After the last payment is made at the end of year five, the funds will stay in the account for four more years. There will be no new payments to the account during the last four years. The interest rate is 6% compounded monthly. What will be the value of the account at the end of nine years? How much interest will the account have earned over the nine years? a) b) 3. Julia has invested a single payment of $8500 in a savings certificate paying a / a) Find the interest rate per conversion interval. guaranteed rate of 3.88% compounded semi-annually for a term of six years. 3 b) Find the future value of the investment at the end of six years. /, c) Find the total interest earned over the six years. 4. Set up the mathematical expression for finding the effective annual rate of 9% compounded monthly. Then evaluate the mathematical expression and express your answer to four places after the decimal point. (Example: 0.1234) 5 You deposit a single payment of $6400 into a savings account. At the end of five years, you have $8200 in the account. Find the nominal rate of interest compounded quarterly earned by the account. 2a)Set up the equation of value. b) Find the nominal rate using the algebraic method. Show all of your steps Express your answer to four places after the decimal point. (Ex: 0.5678)