The Mathematics of Money

46 Chapter 1 Simple Interest

Example 1.5.6 Convert an annual simple interest rate of 9.75% into a daily rate.

Following our default assumption of a 365-day year, we divide by 365: 9.75%/365 

0.02671%.

Be careful not to move the decimal place. In finding interest rates, we get accustomed to

moving the decimal place to convert the decimals used in the formulas to percents. Seeing

0.02671 on the calculator is especially tempting—this result looks like the sort of answer

whose decimal place needs to be moved. But in this case, there is no reason to do so. The

rate is small because a day is a short amount of time.

Converting between Other Units of Time

Suppose that we have a rate per month and want the rate per day, or want to convert from a

rate per month to a rate per week, or from per day to a rate per month, and so on. How do

we handle these conversions? The idea is the same, except that the number we multiply or

divide by will be different.

Example 1.5.7 Convert a simple interest rate of 0.045% per day into a rate per

month. Assume that bankers’ rule is being used.

Under bankers’ rule, we assume that each month has 30 days. Since one month is 30 days,

we multiply 0.045% by 30 to get a rate of 1.35% per month.

Unfortunately, as we’ve seen previously, the calendar poses some problems. Conversions

between monthly and yearly rates are never a problem, because there are always exactly

12 months in a year. But there are not always exactly 30 days in a month. If we were not

using bankers’ rule, we would not have known what to multiply by in Example 1.5.6, since

not all months have the same number of days.

Since annual rates are the norm, though, we seldom have much reason to make a con-

version where neither time unit is years. Therefore, we will not address this matter any

further in this text.

EXERCISES 1.5

A. Using Nonannual Rates

1. Find the interest on a debt of $850.42 for 30 days if the simple interest rate is 0.035% per day.


2. How much interest would you owe on a loan of $4,000 for three weeks if the simple interest rate is 0.0475% per day?


3. If a daily simple interest rate of 0.0225% is charged on a loan of $35,750, how much interest would be paid on a
   1-year loan?


4. Find the interest on a 7-month loan of $5,200 if the simple interest rate is ¾% per month.


5. Jens borrowed $875 for 3 months at a simple interest rate of 0.625% per month. Find the total amount he will need to
   repay the loan.