Copyright © 2008, The McGraw-Hill Companies, Inc.

reason why we need to state the term in months, we will usually convert to days since they

are the most precise time unit that is commonly used.

Example 1.3.3 Suppose that you deposit $3,850 in an account paying 4.65% simple

interest. How long will it take to earn $150 in interest?

I = PRT

$150 = ($3,850)(0.0465)T

$150 = ($179.025)T

T = 0.837871806

This answer is in years. To convert it to more user-friendly terms, we can multiply by 365 to

get the answer in days:

T = (0.837871806)(365) = 306 days

A Few Additional Examples

Now that we have developed tools to work with the simple interest formula, it is worth

working through a few additional examples to get more comfortable.

Example 1.3.4 What amount of money must be invested in a 75-day certifi cate of

deposit paying 5.2% simple interest, using bankers’ rule, in order to earn $40?

I = PRT

$40 = (P)(0.052)(75/360)

$40 = (P)(0.010833333)

__$40

0.010833333

= (P)(0.010833333)____

(0.010833333)

P = $3,692.31

The amount that must be invested is $3,692.31.

Once again, when the numbers run to many decimal places the use of calculator memory

is strongly recommended.

Example 1.3.5 If Shay borrows $20,000 for 9 months and pays interest totaling

$1,129.56, fi nd the rate of simple interest for this loan.

I = PRT

$1,129.56 = ($20,000)(R)(9/12)

$1,129.56 = $15,000(R)

$1,129.56

__

$15,000

=

$15,000(R)

___

$15,000

R = 0.075304

Moving the decimal two places to the right, we fi nd that the rate of simple interest is 7.5304%.

Rounding to two decimal places gives that the rate is 7.53%.

Example 1.3.6 Suppose Michele borrows $4,850 at 6 ¼% simple interest. How long

will it be before her debt reaches $5,050?

I = PRT

$200 = ($4,850)(0.0625)(T)

$200 = $303.125(T)

_____$200

$303.125

= $303.125(T)____

$303.125

T = 0.659793814

Once again, T gives us the time in years, and clearly we need to convert this number to a

more reasonable unit of time. We could try months, but might as well just move directly to

days. Since the problem did not specify bankers’ rule, we’ll assume a 365-day year to get

that the term is (365)(0.659793814) = 241 days.

1.3 Determining Principal, Interest Rates, and Time 27

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