Problem Set: Annuities andPerpetuities(Solutions Below)1. If you plan to save $300 annually for 10 years and thediscount rate is 15%, what is the future value?2. If you want to buy a boat in 6 years that costs $1,000and you can save $150 per year, what interest ratewould you need? 3. If you invest $1,000 per year in a stock portfolio with areturn of 8%, how much would you expect to have in 7years?4. How long would it take you to save $1,000 if youinvested $200 per year, and the interest rate is 10%?5. If you need $10,000 to pay for your first year ofgraduate school in 3 years and you get an interest rateof 9%, how much must you invest each of the nextthree years?6. If 6 years ago you invested $500 and received aninterest rate of 4% (compounded monthly), how muchwould you now have?7. You borrowed $100 from a friend, who said you need topay back $300 in 5 years, what rate are you beingcharged if it is compounded weekly?8. How many years would it take you to have $2,500 ifyou saved $100 each month at 15%?9. To have $6000 in 7 years what interest rate would youneed if you saved $200 every quarter?10. If you win a lottery worth $1,000,000 payable in15 years and the interest rate is 8% (compoundedannually), what is this worth today? Compoundedquarterly? Compounded monthly? Compoundedweekly?11. How long does it take for an investment toquadruple in value if the investment yields 6% per year(compounded monthly)?12. What are the payments on a $40,000 loan repaidmonthly for six year (r = 7%)?13. If I invest $100 today and every quarter for 3years in an account earning 11%, how much will I haveat the end of three years?14. Suppose that I am trying to borrow money fromyou to finance my business, and I promise to repay you$1,000 quarterly for two years. If your opportunity costof funds is 10%, how much are you willing to lend me?15. Jim makes a deposit of $120 every week(beginning next week). The deposit is to earn interestannually at the rate of 9 percent. How much will Jimhave on deposit at the end of seven years?16. How long will it take to repay a loan of $150, if Ipay $1 per week and the rate on my loan is 4%? 17. Value an annuity of $300 per month for 7 years (r= 12.3%).18. Suppose you have the opportunity to make aninvestment expects to pay investors $7,000 per yearfor next eight years. If the cost is $50,000, what returnwould you receive?19. If a two year weekly annuity is worth $5000 and r= 9.8%, what is the weekly cash flow?20. Which grows to a larger future value, $1000invested for 2 years a) at 10 percent compoundedweekly, or b) at 11 percent compounded semi-annually?21. Value an annuity of $40 per year for ten years (r= 13%).22. You want to save for your retirement in 50 years.How much do you need to save from your biweeklypaycheck to have $5 million if you expect a return is7%?23. If an investment is expected to pay $400 permonth for the next 14 months, how much should yoube willing to pay for that asset if your cost of capital is8%?24. You have borrowed $35,000 at an interest rate of9%. If you plan to pay the loan off in annualinstallments of $4,000 (beginning next year), when canyou pay back the loan?25. The type of house you would like to buy requires adown-payment of $50,000. You plan to make that down-payment six years from now. How much do you need tosave per week (beginning next week), if your moneygets 7% (annually)?26. You hope to go to graduate school, and the tuitionwill be $50,000 for the one-year M.B.A. program. If youcan only afford to save $3,000/quarter and the interestrate is 9%, how long will you need to save?27. The house you plan to buy will require a down-payment of $40,000 in two years. How much do youneed to save per month (beginning next month), if yoursavings gets 8% (annually)?28. You have borrowed $10,000 at an interest rate of8.7%. If you plan to pay the loan off in quarterlyinstallments of $1,000 (beginning next quarter), howlong will it take you to pay back the loan?29. Value a perpetuity of $400 per year (r = 14.9%).30. If a perpetuity is worth $1,000 and r = 15.5%,what is the cash flow?Solutions1. If you plan to save $300 annually for 10 years and thediscount rate is 15%, what is the future value?P/Y = 1; N = 10; I/Y = 15; PV = 0; PMT = -300; FV =$6,091.122. If you want to buy a boat in 6 years that costs $1,000and you can save $150 per year, what interest ratewould you need? P/Y = 1; N = 6; I/Y = 4.20%; PV = 0; PMT = -150; FV =1,0003. If you invest $1,000 per year in a stock portfolio with areturn of 8%, how much would you expect to have in 7years?P/Y = 1; N = 7; I/Y = 8; PV = 0; PMT = -1,000; FV =$8,922.804. How long would it take you to save $1,000 if youinvested $200 per year, and the interest rate is 10%?P/Y = 1; N = 4.25 years; I/Y = 10; PV = 0; PMT = 200;FV = -1,0000.25 x 12 = 3  4 years, 3 monthsNOTE: When the question involves time, you mustconvert the answer to ‘x years and y units’.5. If you need $10,000 to pay for your first year ofgraduate school in 3 years and you get an interest rateof 9%, how much must you invest each of the nextthree years?P/Y = 1; N = 3; I/Y = 9; PV = 0; PMT = $3,050.55; FV =-10,0006. If 6 years ago you invested $500 and received aninterest rate of 4% (compounded monthly), how muchwould you now have?P/Y = 12; N = 72 (= 6 x 12); I/Y = 4; PV = -500; PMT =0; FV = $635.377. You borrowed $100 from a friend, who said you need topay back $300 in 5 years, what rate are you beingcharged if it is compounded weekly?P/Y = 52; N = 260 (= 5 x 52); I/Y = 22.02%; PV = -100;PMT = 0; FV = 3008. How many years would it take you to have $2,500 ifyou saved $100 each month at 15%?P/Y = 12; N = 21.89 months; I/Y = 15; PV = 0; PMT =-100; FV = 2,50021.89 ≈ 22 months  1 year, 10 monthsNOTE: Since N is periods, the time unit is the paymentperiod.9. To have $6000 in 7 years what interest rate would youneed if you saved $200 every quarter?P/Y = 4; N = 28 (= 7 x 4); I/Y = 2.02%; PV = 0; PMT =-200; FV = 6,00010. If you win a lottery worth $1,000,000 payable in15 years and the interest rate is 8% (compoundedannually),