Compound Interest

I assume you have studied simple interest in school. Now, let us recall that. The interest of principle P in time T years with of interest R was;

We don't add interest in principle while calculating simple interest. If we add interest in principle so as to make new principle on a routine basis, this is called compound interest.

If we add interest after one year as routine then;

after one year;

A = P+ I = P + PR/100 = P(1+R/100)

This is new principle now;

after two years;

A = P(1+R/100) + P(1+R/100)*R/100 = P(1+R/100)(1 + R/100) = P(1+R/100)^2

after three years;

A = P(1+R/100)^2 + P(1+R/100)^2 R/100 = P(1+R/100)^2( 1+ R/100) = P(1+R/100)^3

generalizing this;

A = P(1+R/100)^T for T years.

This result is compounded once a year. If we compounded n times in a year then more generalized result is;

A =P(1+ R/100 n)^nT

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Example:

Hari takes a loan of $1,000 to buy a used truck at the rate of 5 % simple Interest. He paid total amount after 5 years. How much did he pay if

i. Interest was simple

ii. Interest was compounded yearly:

Solution:

principle = $ 1000

time = 5 years

Rate = 5 %

simple interest(SI) = PTR/100 = 100055/100 = $ 250

Amount(A1) = 1000 + 250 = $ 1250

compound amount = P(1 +r/100)^T = 1000(1+5/100)^5 = $ 1276.281

compound interest = 1276.281-1000 = $ 276.281

Since interest is added in principle, compound interest is greater than simple interest. For one year; compound interest yearly us equal to simple interest.

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1. Image source: http://blog.talentsprint.com/2017/04/interest-ii-how-to-find-simple-interest.html

2. http://www.investopedia.com/terms/c/compoundinterest.asp