Interests and Installments

Simple Interest = (Principal * rate * time)/100.

Amount = Principal * [1 + (rate*time)/100].

Compound interest = Amount – Principal.

Amount under compound interest = Principal * [1 + r/(x*100)] ^(x*t).

Amount under compound interest (half-yearly) = Principal * [1 + r/ (2*100) ]^(2*t).

Amount under compound interest (quarterly) = Principal * [1 + r/(4*100) ]^(4*t). 

Simple Interest in instalments : A = [ x + (x + x*r*1/100) + (x + x*r*2/100) + …]
= P + P*n*r/100, n is the number of instalments and x = value of each instalment.

Compound Interest in instalments : P = [ x/(1+r/100) + x/(1+r/100)^2 + … + x/(1+r/100)^n.

Amount = P(1+r/100)^n.

Difference between CI and SI for n-th year = (P*r/100) * [(1+r/100)^(n-1)  1].

(Increase in amount in nth year/Increase in amount in (n+1)-th year) = 100/(100+r). 

(Decrease in amount in nth year/Decrease in amount in (n+1)-th year) = 100/(100+r).