Formula for Compound Interest, Population Growth and Depreciation

Compound Interest 

If Principal =P, Compound Amount = CA, Rate of interest =R, Time= T and Compound Interest Interest= CI then,

 If Interest is calculated annually;
1. CA=P(1+R/100)^T

      [ Interest is being calculated annually]
2. CI= P[(1+R/100)^T-1]
 If Interest is calculated Semi-annually
3. CA=P[(1+R/200)^2T]

4. CI= P[(1+R/200)^2T-1]

If Time is given In T years and M months then,
5.CA=P(1+R/100)^T(1+MR/1200)
6.CI=P[(1+R/100)^T(1+MR/1200)-1]

Special cases
7. CI= CA-P
8. P=CA-CI
9. CA= P+CI

Population Growth

If Initial population = P, Final population/Population after T years= P_T Rate of growth  =R, and Time = T then,

1.P_T  = P(1+R/100)^T

2.P_T  = P(1+R₁/100)(1+R2/100)(1+R3/100) if growth rate is R₁%, R₂% and R₃% respectively given for the first, second and third year respectively.
3. Population growth rate= Birth rate - Death rate.
4. P_T  = P(1+R/200)^T- M_in-M_out  where M_in and M_out are in migration and out migration respectively.

Depreciation

If Initial value = P, Value after T years= D_T Rate of depreciation =R, and Time = T then,
1.D_T  = P(1- R/100)^T

2.D_T  = P(1-R₁/100)(1-R2/100)(1-R3/100) if depreciation rate is R₁%, R₂% and R₃% respectively given for the first, second and third year respectively.
3. Amount of depreciation= Initial value- Price after depreciation.