ThegreatAlbertEinsteinoncesaid“Compoundinterestistheeighthwonderofthe world. He who understands it earns it...he who doesn't...pays it.” Whatisthefuture value of an initial $500 after 30 years if it is invested in an account paying 15 percent annual interest? What is the present value of $1000000 to be received in 15 years if the appropriate interest rate is 12 percent?
Assume that you are nearing graduation and that you have applied for a job at a local bank. As part of the bank’s evaluation (interview) process, you have been asked to take an exam that covers several financial analysis techniques. The hiring decision depends on how you would answer the following questions:
Part I: TVM Analysis. The first section of the test addresses time value money analysis.John andMaryareayoungcouple, who want to put their finance in order. Boththehusbandandthe wifeare27yearsagoandinstableemployment. They want to manage their savings and earnings to achieve a better return and reduce the risks. You want to help them with their financial planning by answering a series of questions as follows:
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ThegreatAlbertEinsteinoncesaid“Compoundinterestistheeighthwonderofthe world. He who understands it earns it...he who doesn't...pays it.” Whatisthefuture value of an initial $500 after 30 years if it is invested in an account paying 15 percent annual interest? What is the
present value of $1000000 to be received in 15 years if the appropriate interest rate is 12 percent? -
What is the difference between an ordinary
annuity and an annuity due? What are thefuture value and present value of a five-year ordinary annuity of $1000 if the appropriate interest rate is 10 percent? What would the future and present values be if the annuity were an annuity due? -
Willthefuturevaluebelargerorsmallerifwecompoundaninitialamountmoreoften than annually—for example, every six months, or semiannually—holding the stated interest rate constant? Why? What is the effective annual rate for a simple rate of 12 percent, compounded semiannually? Compounded quarterly? Compounded daily?
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Suppose someone offered to sell you a note that calls for a $1,000 payment 15 months from today. Thepersonofferstosell thenotefor$850.Youhave$850inabanktime a deposit (savings instrument) that pays a 6.76649 percent simple rate with daily compounding, which is a 7 percent effective annual interest rate; and you plan to leave this money in the bank unless you buy the note. The note is not risky—that is, you are sure it will be paid on schedule. Should you buy the note? Check the decision in both ways: (1) by comparing your future value if you buy the note versus leaving your money in the bank, (2) by comparing the PV of the note with your current bank investment.
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