Compound Interest Questions

FACTS  AND  FORMULAE  FOR  COMPOUND  INTEREST  QUESTIONS

Let Principal = P, Rate = R% per annum, Time = n years.

I.

1.  When interest is compound Annually:

Amount =$P{\left(1+\frac{R}{100}\right)}^n$

2.  When interest is compounded Half-yearly:

Amount = $P{\left[1+\frac{\left({\displaystyle \raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}{100}\right]}^{2n}$

3.  When interest is compounded Quarterly:

Amount = $P{\left[1+\frac{\left({\displaystyle \raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\right)}{100}\right]}^{4n}$

II.

1.  When interest is compounded Annually but time is in fraction, say $3\frac{2}{5}$ years.

Amount = $P{\left(1+\frac{R}{100}\right)}^3\times \left(1+\frac{{\displaystyle \frac{2}{5}}R}{100}\right)$

2.  When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then, Amount = $P\left(1+\frac{R_1}{100}\right)\left(1+\frac{R_2}{100}\right)\left(1+\frac{R_3}{100}\right)$

III.  Present worth of Rs. x due n years hence is given by:

Present Worth = $\frac{x}{{\left(1+{\displaystyle \frac{R}{100}}\right)}^n}$