Simple Interest

Simple Interest
In simple interest, only the original principal bears interest and the interest to be paid varies directly with time.
 

The formula for simple interest is given by

$I = Prt$

 

The future amount is

$F = P + I$

$F = P + Prt$

$F = P(1 + rt)$

 

Where
$I$ = interest
$P$ = principal, present amount, capital
$F$ = future amount, maturity value
$r$ = rate of simple interest expressed in decimal form
$t$ = time in years, term in years
 

Ordinary and Exact Simple Interest
In an instance when the time t is given in number of days, the fractional part of the year will be computed with a denominator of 360 or 365 or 366. With ordinary simple interest, the denominator is 360 and in exact simple interest, the denominator is either 365 or 366. We can therefore conclude that ordinary interest is greater than exact interest.
 

Note:
When simple interest (ordinary or exact) is not specified in any problem, it is assumed as ordinary.

 

Ordinary simple interest is computed on the basis of banker’s year.

Banker’s year
1 year = 12 months
1 month = 30 days (all months)
1 year = 360 days

 

Exact simple interest is based on the actual number of days in a year. One year is equivalent to 365 days for ordinary year and 366 days for leap year. A leap year is when the month of February is 29 days, and ordinary year when February is only 28 days. Leap year occurs every four years.
 

Note:
Leap years are those which are exactly divisible by 4 except century years, but those century years that are exactly divisible by 400 are also leap years.
 

If d is the number of days, then ...
In ordinary simple interest
  • $t = \dfrac{d}{360}$

 

In exact simple interest
  • $t = \dfrac{d}{365}$       (for ordinary year)
     
  • $t = \dfrac{d}{366}$       (for leap year)

 

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