The Mathematics of Money

Because these different methods do give different results, it is important to be clear on

which method is being used in any given situation. Even though the differences are not big,

it is easy to see how confusion and disputes could arise if the choice of method were left

unclear. In practice, if the term of the loan is to be measured in days, the terms of the loan

should specify which method will be used in order to prevent misunderstanding.

You might suspect that the differences between bankers’ rule and the exact method leave

an opportunity for sneaky banks to manipulate interest calculations to their benefit. After all,

what prevents a bank from always choosing whichever rule works to its advantage (and thus

to the customer’s disadvantage)? In practice, the method to be used will be specified either in

a bank’s general policies, government regulations, or in the paperwork for any deposit or loan,

and in any case, as we’ve seen above, the difference is slight. It is probably true that some

banks select one method or the other to nudge things to their favor, but their benefit from doing

this would be minimal. A bank that wants to pay less interest on a deposit or charge more on

a loan won’t get very far playing games with the calculation method, and is far more likely to

just charge a higher or pay a lower rate pure and simple. In any case, an informed consumer

can (and should) use mathematics to compare different rates and calculation methods.

Loans with Other Terms

It is possible to measure the term of the loan with units other than years, months, or days.

While such situations are far less common, they can be handled in much the same way.

Example 1.2.8 Bridget borrows $2,000 for 13 weeks at 6% simple interest. Find the

total interest she will pay.

The only difference between this problem and the others is that, since the term is in weeks,

we divide by 52 (since there are 52 weeks per year).

I  PRT

I  ($2000)(0.06)(13/52)

I  $30

So Bridget’s interest will total $30.

There is some ambiguity here, though. A year does not contain exactly 52 weeks; 52 weeks

times 7 days per week adds up to only 364 days. Each year thus actually contains 52^1 ⁄ 7 (or,

if it is a leap year, 52^2 ⁄ 7 ) weeks. Since weeks are not often used, there is no single standard

accepted way of dealing with the extra fractional weeks. In this text we will follow the

reasonable approach used above, and simply assume 52 weeks per year.

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

A. Loans with Terms in Months

1. Find the interest that would be paid for a loan of $1,200 for 6 months at 10% simple interest.


2. If Josh loans Adam $500 for 8 months at 5.4% simple interest, how much interest will Adam pay?


3. Allison loaned Lisa $15,453 for 22 months. The simple interest rate for the loan was 11^5 ⁄^8 %. Find the total amount of
   interest Allison earned.

EXERCISES 1.2

Exercises 1.2 17