11. Calculate annuity cash flows Your goal is to have $15,000 in your bank account by the end of 10 years. If the interest rate remains constant at 9% and you want to make annual identical deposits, how much will you need to deposit in your account at the end of each year to reach your goal? (Note: Round your answer for PMT to two decimal places.) $1,086.03 $1,184.76 $987.30 $789.84 If your deposits were made at the beginning of each year rather than an at the end, by how much would the amount of your deposit change if you still wanted to reach your goal by the end of 10 years? (Note: Round your answer for PMT to two decimal places.) $110.05 $81.52 $101.90 $61.14 10. Future value of annuities When payments are made at the end of each period, you will treat them as an ordinary annuity - You are planning to put $2,000 in the bank at the end of each year for the next eight years in hopes that you will have enough money for a new boat. If you are investing at an annual interest rate of 6%, you'll have accumulated at the end of eight years. You decided to deposit your money in the bank at the beginning of the year instead of the end of the same year, but now you are making payments of $2,250 at an annual interest rate of 8%. How much money will you have available at the end of four years? $16,509 $10,950 $15,874 $15,304 12. Present value of annuities You won a lottery that will make equal payments of $3,500 at the end of each year for the next ten years. If the annual interest rate stays constant at 5%, what is the value of these payments in today's dollars? Round your answer to the nearest whole dollar. $22,972 $28,377 $27,026 $33,783 You found out that now you are going to receive payments of $8,500 for the next 11 years. You will receive these payments at the beginning of each year. The annual interest rate will remain constant at 11%. What is the present value of these payments? Round your answer to the nearest whole dollar. $52,755 $79,053 $46,846 $58,558 13. Present value of annuities and annuity payments The present value of an annuity is the sum of the discounted value of all future cash flows. You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $500 at the end of every six months An annuity that pays $500 at the beginning of every six months An annuity that pays $1,000 at the beginning of each year An annuity that pays $1,000 at the end of each year An ordinary annuity selling at $10,538.38 today promises to make equal payments at the end of each year for the next twelve years (N). If the annuity's appropriate interest rate (1) remains at 6.50% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won -assuming annual interest rate of 6.50%. (Note: Round intermediate calculations to the nearest whole number.) 14. Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration Joshua needed money for some unexpected expenses, so he borrowed $5,958.17 from a friend and agreed to repay the loan in six equal installments of $1,250 at the end of each year. The agreement is offering an implied interest rate of Joshua's friend, Willie, has hired a financial planner for advice on retirement. Considering Willie's current expenses and expected future lifestyle changes, the financial planner has stated that once Willie crosses a threshold of $14,836,230 in savings, he will have enough money for retirement. Willie has nothing saved for his retirement yet, so he plans to start depositing $100,000 in a retirement fund at a fixed rate of 7.00% at the end of each year. It will take years for Willie to reach his retirement goal. 15. Mortgage payments Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump-sum amount as a loan in the beginning, and then you make monthly payments to the lender. You've decided to buy a house that is valued at $1 million. You have $250,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $750,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be per month. (Note: Round the final value of any interest rate in percentage form to four decimal places.) Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $750,000 loan at a fixed nominal interest rate of 10% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be (Note: Round the final value of any interest rate in percentage form to four decimal places.) It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage? $1,083,545.86 $1,267,197.70 $918,259.20 $1,175,371.78