Simone runs a small business and receives an invoice for $2000 with terms 2/20, n/60. If Simone doesn't pay immediately and instead pays in 60 days, what effective annual interest rate is she paying? Use the daycount convention ACT/365. Wing Sze is saving for her retirement. She puts her money in an account paying 9.5% interest compounded annually. a) After 25 years she has exactly $1,000,000. How much money did she start out with? (To the nearest $0.01) b) If instead of annual compounding, her account paid 9.5% compounded monthly, how many months sooner would she have reached her goal of (at least) $1,000,000? You win the lottery! Your choices are Take a single payment of $25 million today. Take 25 payments of $2 million, first payment today and then $2 million at the start of every year for the next 24 years a) If the interest rate is 2% compounded annually, which would you prefer? b) If the interest rate is 9% compounded annually, which would you prefer? c) At what annually compounded interest rate (to 5 decimal places) would you be indifferent between the two? (Hint: You will probably want to build a spreadsheet to compute the present value of each of the $1 million payments, and then add them up. You can part c) by trial and error, or by using the spreadsheets goal seek function.) Ricardo and Bart open savings accounts that both pay the same annually compounded rate of interest i. Ricardo deposits $700 initially and Bart deposits $1400. The amount of interest Bart earns in year 7 is X, the same amount that Ricardo earns in year 14. a) Write down an equation for At), the accumulation amount for each of their accounts. b) Solve for i. c) Solve for X. A discounted note that pays $32000 in 6 months sells for X. Find X in each of the following interest rate scenarios: a) simple interest at an annual rate of 6% b) simple discount at an annual rate of 6% c) compound interest at a nominal rate of 6% compounded semi-annually d) compound interest at a nominal rate of 6% compounded monthly e) Are any of your answers to the above exactly the same? If so, can you explain why? Simone runs a small business and receives an invoice for $2000 with terms 2/20, n/60. If Simone doesn't pay immediately and instead pays in 60 days, what effective annual interest rate is she paying? Use the daycount convention ACT/365. Wing Sze is saving for her retirement. She puts her money in an account paying 9.5% interest compounded annually. a) After 25 years she has exactly $1,000,000. How much money did she start out with? (To the nearest $0.01) b) If instead of annual compounding, her account paid 9.5% compounded monthly, how many months sooner would she have reached her goal of (at least) $1,000,000? You win the lottery! Your choices are Take a single payment of $25 million today. Take 25 payments of $2 million, first payment today and then $2 million at the start of every year for the next 24 years a) If the interest rate is 2% compounded annually, which would you prefer? b) If the interest rate is 9% compounded annually, which would you prefer? c) At what annually compounded interest rate (to 5 decimal places) would you be indifferent between the two? (Hint: You will probably want to build a spreadsheet to compute the present value of each of the $1 million payments, and then add them up. You can part c) by trial and error, or by using the spreadsheets goal seek function.) Ricardo and Bart open savings accounts that both pay the same annually compounded rate of interest i. Ricardo deposits $700 initially and Bart deposits $1400. The amount of interest Bart earns in year 7 is X, the same amount that Ricardo earns in year 14. a) Write down an equation for At), the accumulation amount for each of their accounts. b) Solve for i. c) Solve for X. A discounted note that pays $32000 in 6 months sells for X. Find X in each of the following interest rate scenarios: a) simple interest at an annual rate of 6% b) simple discount at an annual rate of 6% c) compound interest at a nominal rate of 6% compounded semi-annually d) compound interest at a nominal rate of 6% compounded monthly e) Are any of your answers to the above exactly the same? If so, can you explain why