Engineering Economic Analysis

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Time Value of Money 65

Youhave agreedto loan a friend $5000 for 5 years at a simple interest rate of 8% per year. How

much interest will you receive from the loan'? How much will your friend pay you at the end of

5 years?

Total interest earned= Pin = ($5000)(0.08)(5 yr) - $2000

Amount due at end'of loan = P+ Pin = 5000 + 2000 = $7000

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In Example 3-3 the interest earned at the end of the first year is (5000)(0.08)(1) = $400, but

this money is not paid to the lender until the end of the fifth year. As a result, the borrower

has the use of the $400 for four years without paying any interest on it. This is how simple

interest works, and it is easy to see why lenders seldom agree to make simple interest loans.

Compound Interest

With simple interest, the amount earned (for invested money) or due (for borrowed money)

in one period does not affect the principal for interest calculationsin later periods. However,

this is not how interest is normally calculated. In practice, interest is computed using

the compound interest method. For a loan, any interest owed but not paid at the end

of the year is added to the balance due. Thus, the next year's interest is calculated based on

the unpaid balance due, which includes the unpaid interest from the precedingperiod. In this

way, compound interest can be thought of asinterest on top of interest.This distinguishes

compound interest from simple interest. In this section, the remainder of the book, and in

practice you should assume that the rate is a compound interest rate. The few exceptions

will clearly state use "simple interest."

To highlight the differencebetween simple and compound interest, rework Example 3-3 using an

interest rate of 8% per year compound interest. How will this change affect the amount that your

friend pays you at the end of 5 years?

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Original loan amount (original principal)=$5000

Loan term=5 years

Int~rest rate charged 8%per year cOlnpound interest
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