Finding the required interest rate Your parents will retire in 19 years. They currently have $240,000, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places. % Future value of an annuity Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent. a. $200 per year for 12 years at 16%. b. $100 per year for 6 years at 8%. c. $500 per year for 10 years at 0%. Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent. d. $200 per year for 12 years at 16%. e. $100 per year for 6 years at 8%. $ f. $500 per year for 10 years at 0%. Present value What is the present value of a security that will pay $9,000 in 20 years if securities of equal risk pay 8% annually? Round your answer to the nearest cent. $ Present and future values for different periods Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Round your answers to the nearest cent. a. An initial $400 compounded for 1 year at 8%. $ b. An initial $400 compounded for 2 years at 8%. $ c. The present value of $400 due in 1 year at a discount rate of 8%. $ d. The present value of $400 due in 2 years at a discount rate of 8%. $ Time for a lump sum to double If you deposit money today in an account that pays 14% annual interest, how long will it take to double your money? Round your answer to two decimal places. years Future value: annuity versus annuity due a. What's the future value of a 12%, 5-year ordinary annuity that pays $600 each year? Round your answer to the nearest cent. $ b. If this was an annuity due, what would its future value be? Round your answer to the nearest cent. $