# A company rece i ves cash today and promises to make

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A company receives cash today and promises to make periodicinterest pay·ments over time and a principal payment at the bond's maturity.A company receives the use of a product or property and promises lo makeperiodic payments to the party from whom it obtained the use of the productor property.A company promises to pay employees a certain amount after they retire.We begin our discussion of the ti111e value of money by distinguishing between two types ofinterest-simple andcompo1111d.
EXAMPLE 7.1Simple InterestPROBLEM:Solin1de Company borrows \$60,000 for 3 years wiih a stated annual rate of 5%. Whatis the intere.st expense incurred by Solitude, assuming that interest is computed as simple interest?Accounting and the Time Value of Money317Simple InterestThe termsimple interestmeans that interest is computed on only the principal (the initial amount)but is not computed on any interest ean1ed and left on deposit Thus,simple interestis the initialinvestment multiplied by the stated interest rate for a single period and the amount of time (interms of the nmnber of periods) the investment is held.Si1nple Interest=PrincipalXInterest RateXTime(7.1)Time
Compound InterestInterest co1nputed on both the principal and the interest left on deposit is refen-ed to ascompoundinterest.Any interest earned is then immediately included in the computation of the next period'sinterest. The compounding period can be over any time period such as a quarter or a day.Exhibit 7.2 provides a graphical depiction of compound interest. Assume you invest \$ I 00today for IO years at an annual interest rate of 10%. Today (Year 0) you have\$ JOO. After the firstyear, you have the original \$100 plus an additional \$IO (\$100 X 10%) of interest. So, you nowleave \$ IIO on deposit.During the second year, that \$110 also earnsI0%interest or\$ II(\$I IOXl0%).At the endof the second year, your depositisvalued at\$121 (\$100+\$IO+\$1 I). This pattern continuesuntil the tenth year,when you have a total of\$259, which consists of your original deposit or prin-cipal of\$ I 00 plus\$100 of interest earned on the principal (\$100 X I 0% X IO years) and\$59 ofinterest earned on the interest left on deposit. If this investment earned only simple interest, yourtotal value at the end of the tenth year would be \$200. That is, interest would be earned only onthe principal (\$100=\$100 X I 0% X IO years), not on the interest left on deposit. Therefore.co1npounding increases your retm11 by \$59 and increases youreffective interest rate.EXHIBIT 7.2Compound Interest300 ,;::======;--- - - -7Interest on Interest250Interest on PrincipalPrincipal:,..

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