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FIN 3087 Chapter 5 homework




Question;1.You deposit $5,000 in an account that earns 12% compounded annually. Compute theaccount balance at the end of:a.b.c.1 year20 years40 yearsFUTURE VALUE2.You deposit $100,000 in an account that earns a 10% annual rate of return. You havedecided that at the end of each year you will withdraw the interest that is credited to youraccount. If you plan on closing the account at the end of the tenth year, how much are youable to withdraw at that point in time?FUTURE VALUE, EFFECTIVE RATE CALCULATION IS REQUIRED3.You have the opportunity to deposit $10,000 into one of two accounts. The Optimumaccount offers to pay 12% compounded annually while the prime account offers to pay 12%compounded monthly. If you plan on leaving the money in the account for 10 years, whatwill be the difference between the Optimum and Prime account balances at the end of thetenth year?PRESENT VALUE4.If you expect to inherit $50,000 at the end of the 20 years, compute the present value of theinheritance at the following annual interest rates.a.b.c.6%12%24%5-1Name:___________________________FIN3087Date:_________________PRESENT VALUE5.If you require a 10% rate of return on the following investment opportunities, which wouldyou prefer--$100,000 today, $250,000 ten years from today, or $12,000 per year at the endof each of the next 20 years?PRESENT VALUE, EFFECTIVE RATE CALCULATION IS REQUIRED6.Mirage Investments is offering a investment opportunity that pays a 10% annual rate ofreturn, compounded quarterly. How much would you have to pay for this investment ifMirage has agreed to pay you $32,000 at the beginning of the sixth year?DETERMINATION OF THE NUMBER OF TIME PERIODS7.How long will it take to double your initial deposit into an Escalator Account, if the bankoffering the account pays the following interest rates:a.b.c.9% compounded annually14% compounded annually9% compounded monthlyDETERMINATION OF THE NUMBER OF TIME PERIODS8.Insolvent Savings and Loan has advertised an account that pays 8% compounded annually.In the ad, Insolvent provides a example of a hypothetical account. The ad shows that acustomer depositing $10,000 with the bank can achieve an account balance of $100,627.Due to a misprint, it is not clear from the ad how long a customer would have to leave themoney in the account.It is up to you to correct that misprint--how long does thishypothetical customer have to leave the money in the account?INTEREST RATE DETERMINATION9.Compute the effective annual interest rate paid by your bank if your initial deposit with thebank doubles in:a.b.c.5 years10 years20 years5-2Name:___________________________FIN3087Date:_________________INTEREST RATE DETERMINATION10. Over a 13 year time period, your $3,000 investment in gold coins has increased in value to$15,000. What effective annual rate of return have you earned on your investment in gold?What is your holding period return on this investment?PRESENT VALUE OF AN ANNUITY11. Mutual Benefit is offering a "Ultimate Opportunity" annuity contract that offers investors a14% annual rate of return. The contract specifies that Mutual Benefit will pay the investoran equal amount at the end of each contract year. You have decided to buy a contract thatprovides an annual payment of $10,000 per year at the end of each of the next 20 years.How much are you going to have to pay Mutual Benefit for this annuity contract?PRESENT VALUE OF AN ANNUITY12. You just lost a lawsuit which requires you to pay the plaintiff $500,000. The judge, notbeing well versed in finance, has agreed to your request that you be allowed to pay $25,000per year at the end of each of the next 20 years.a.b.c.If you can invest in government securities that compound interest at an annual rate of7%, how much do you have to set aside today in order to insure that the payments aremade to the plaintiff?If your broker tells you that by investing in securities issued by corporations you canearn a compound annual rate of 12%, how much do you have to set aside today in orderto insure that the payments are made to the plaintiff?Which investment alternative would you select? Should the plaintiff care about yourdecision?FUTURE VALUE OF AN ANNUITY13. You have decided to deposit $1,000 per year at the end of each of the next 15 years in anaccount that earns 5% compounded annually. What is the account balance at the end of thefifteenth year?FUTURE VALUE OF AN ANNUITY14. Since the big promotion and the raise that goes with it finally came through, you havedecided to get serious about saving some money. You are going to save $5,000 per year atthe end of each of the next 25 years, but are unsure where to invest the money. If you investthe money in certificates of deposit, you forecast that you will earn a 7.5% effective annualrate of return. An alternative is to invest the money in a High Yield bond fund. The fundclaims that last year it generated a 14% effective annual rate of return, but notes that pastperformance may not reflect future returns.5-3Name:___________________________FIN3087Date:_________________a. Compute the account balance at the end of the twenty-fifth year if you select thecertificate of deposit investment alternative.b. Compute the account balance at the end of the twenty-fifth year if you select the HighYield investment alternative. Assume that the fund earns a 14% annual return.c. Given the difference in the account balances, why would anyone purchase certificatesof deposit?PRESENT VALUE OF ANNUITY DUE15. Three years ago you borrowed $30,000 in order to purchase a boat. The lender agreed to a 7year loan at a 14% annual interest rate. A unique feature of the loan is the requirement thatthe annual payment of $6,136.64 be made at the beginning of each year. It is the end of thethird year and you are about to write a check for the fourth payment. Since this last yearwas fairly prosperous you have decided to pay off the entire loan balance at this time. Howmuch do you have to pay in order to repay the entire remaining balance on the loan?FUTURE VALUE OF AN ANNUITY DUE16. You have decided to deposit $1,500 per year at the beginning of each of the next 10 years inan account that earns 8% compounded annually. What is the account balance at the end ofthe tenth year?


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