Earning, Spending and Simple Interest

A wage is paid by the hour. Overtime hours are paid at a higher rate: time-and-a-half means one and a half times the normal rate, and double time means twice the normal rate. Suppose you earn twenty-four dollars an hour, work thirty-eight normal hours, and four hours at time-and-a-half. The normal hours earn thirty-eight times twenty-four, which is nine hundred and twelve dollars. The overtime rate is one and a half times twenty-four, thirty-six dollars an hour, so four hours earn one hundred and forty-four dollars. Your gross pay is one thousand and fifty-six dollars. Always work out each block of hours separately, then add.

Salespeople are often paid commission, which is a percentage of the value of what they sell. Many also get a retainer, a fixed amount paid whether they sell anything or not. With a four hundred dollar retainer and five percent commission on twelve thousand dollars of sales, the commission is nought point nought five times twelve thousand, which is six hundred dollars. Add the retainer, and the pay is one thousand dollars. A quick check: one percent of twelve thousand is one hundred and twenty, so five percent is six hundred.

Simple interest is the same amount of interest every year, worked out on the original amount only. The formula is I equals P R N. P is the principal, the amount you invest or borrow. R is the interest rate per year, written as a decimal. N is the number of years. For three thousand dollars at five percent per annum for four years, I equals three thousand times nought point nought five times four, which is six hundred dollars. Each year earns one hundred and fifty dollars. The total amount at the end is the principal plus the interest: three thousand six hundred dollars.

The rate in I equals P R N is per annum, which means per year. So N has to be in years. Nine months is nine twelfths of a year, which is nought point seven five. For six thousand dollars at eight percent for nine months, one full year of interest would be four hundred and eighty dollars, and three quarters of that is three hundred and sixty dollars. If you put nine in for N, you get four thousand three hundred and twenty dollars, which is far too much for less than a year. Always sense-check: less than a year must earn less than one year's interest.

You can run the formula backwards to find any missing letter. If two thousand five hundred dollars earns four hundred and fifty dollars in three years, put the numbers in: four hundred and fifty equals two thousand five hundred times R times three. Two thousand five hundred times three is seven thousand five hundred, so R is four hundred and fifty divided by seven thousand five hundred, which is nought point nought six, or six percent per annum. To find the principal, divide the interest by R times N: two hundred and eighty dollars of interest at four percent for two years needs two hundred and eighty divided by nought point nought eight, which is three thousand five hundred dollars. Quiz and exercises now.