# Formula to calculate ordinary and exact rate of interest

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Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year. The interest formulas for both ordinary and exact interest are actually the same, with time slightly differing when given as number of days.

Interest is the sum paid for the use of money. Business concerns and individuals who find themselves in need of cash or financial credit borrow money and agree to pay a certain percentage for the privilege of using the borrowed amount.

Interest is computed on an agreed rate of interest. It is a certain percent of the sum borrowed called the principal. After the interest period or loan period is over, the money-lender would receive the original amount of the loan together with the agreed interest.

In simple interest, the basic equation is: Interest = Principal x Rate. However, there is the element of time which also plays a significant part in interest problems. Thus, the basis of equation is modified to: Interest = Principal x Rate x Time.

Time is to be expressed in number of years or as part of a year. When time is given in terms of months, it is easily converted to a fractional year by using the equivalence 1 year = 12 months.

But when time is given in terms of days, two possible equivalence may be used:

- 360 days = 1 year
- 30 days = 1 month
- 365 days = 1 year

Commercial firms and banks often use ordinary interest. Problems on exact interest specify that the interest required is exact; those not qualifying the kind of interest needed are taken to mean ordinary interest. Formulas to be used will be:

**I = Prt **where P = principal (original sum), r = rate of interest and t = time expressed in years

- I. = Pr (D/360); I. = ordinary interest, D = no. of days
- I. = Pr (D/365); I. = exact interest

**F = P + I** where F = final amount to be paid

Sample problems:

What is the **ordinary interest** on $1,360 for 90 days at 4%? Given: P = $1,360, r = 4%, D = 90 days

- Solution: I. = Pr (D/360); I. = $1,360 x 90/360 x 4/100; I. = $13.60

Find the **exact interest** on $500 at 8% for 45 days. Given: P = $500, r = 8%, D = 45 days

- Solution: I. = Pr (D/365); I. = $500 x 8/100 x 45/365; I. = $4.93

Nowadays borrowing money is already a trend, so borrowers should at least become familiar to the different calculations of interests for the ordinary interest and exact interest for the money they wanted to borrow from any banks and other financing agencies.

Source of idea: my old personal notes when I took up Business Mathematics

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