The Mathematics of Money

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

c. Since Tom and Jerry both had the same amount of money, the same amount of time, and the same interest rate, it

would seem that they should both have ended up with the same amount of money. Why didn’t they?

40. Mireille has been offered the opportunity to own a restaurant franchise. Right now, she makes $60,000 per year as
    a computer analyst, but she projects that she would be able to earn $85,000 annually by quitting her current job and
    working full time managing the restaurant. However, she would need to invest $500,000 in the business up front.
    If she were to invest this money elsewhere, she believes she could earn 7% simple interest per year on her money.
    Would she really be making more money from the franchise? Explain.


41. Determine the simple interest for a $2,000 loan at 5.25% for 6 months.


42. Determine the simple interest for a loan of $5,250 for 1 year if the simple interest rate is 1.25% per month.

1.2 The Term of a Loan 13

1.2 The Term of a Loan

So far, we’ve considered only loans whose terms are measured in whole years. While

such terms are not uncommon, they are certainly not mandatory. A loan can extend for

any period of time at all. When the interest rate is per year, and the term is also in years,

we hardly even need to think about the units of time at all. When dealing with loans

whose terms are not whole years, though, we have to take a bit more care with the units

of time.

Loans with Terms in Months

It stands to reason that the units of time used for the interest rate must be consistent with the

units used for the term. Since interest rates are normally given per year, this usually means

that we must convert the term into years to be consistent. The following example will

illustrate how we have to handle a loan when the term is not a whole number of years.

Example 1.2.1 If Sarai borrows $5,000 for 6 months at 9% simple interest, how

much will she need to pay back?

As before, we can calculate her interest by using I  PRT, plugging in P  $5,000 and R 

0.09. T is a bit more complicated. We must be consistent with our units of time.

The term is 6 months, but we can’t just plug in T  6, since the 9% interest rate is assumed

to be a rate per year. Since the interest rate is per year, when we use it we must measure

time in years. Plugging in T  6 would mean 6 years, not 6 months.

T should give the term of the loan in years. Since a year contains 12 months, 6 months is

equal to^6 ⁄ 12 of a year, and so we plug in T  6/12. (Another way of looking at this would be

to say that since 6 months is half of a year, T  1/2. Either way, we get the same result since

6/12  1/2  0.5.)

Thus

I  PRT

I  ($5,000)(0.09)(6/12)