Compound interest: Money is said to be lent at compound interest if the interest is not paid as soon as it falls due but is added to the principal after a fixed period and the amount thus obtained becomes the principal for the next period, this process is repeated until the amount for the last period has been obtained. Thus, the difference between the original principal and the final amount is called the compound interest.
Principal: The money borrowed is called Principal or Sum.
Simple interest: The extra money given by the borrower for the privilege of having used the money is called Interest.
Amount: Amount = Principal + Interest.
Rate percent: Interest on Rs. 100 for 1 year is called rate per cent per annum.
Important formula's for simple Interest: If P, R, T stand for principal, rate and time respectively and S.I. stands for simple interest then
(i) S.I. = (P * R * T)/100
(ii) P = 100*S.I. / R*T
(iii) R=100*S.I. / P*T
(iv) T= 100*S.I. / P*R
For compound interest: Compound Interest = (Amount) - (Principal).
If Principal = Rs. P, Rate = R% p.a. and Time = T years, then
(i) Amount after T years (Compounded annually) = P (1+(R/100)T
(ii) Amount after T years (Compounded half-yearly)
= P (1+(R/2)/100)2T
(iii) Amount after T years (Compounded quarterly)
= P (1 + (R/4) / 100)4T
(iv) If the rates be p%, q%, r% during first year, second year and third year, then Amount after 3 years
= P (1 + P/100) (1 + q/100) (1 + r/100)
Rate of growth: = increase inpopulation / original population
This average increase is called the rate of growth.
Note:
(i) There is no difference between S.I. and C.I. and on any sum at the, rate per annum for one (first) year.
The compound interest and simple interest on the same sum at the same rate remains the same for first payable period. So also for their amounts.
(ii) The difference between the compound interest and the simple interest for 2 years = Simple interest for 1 year on 1st year's interest.
(iii) The previous year's amount is the principal for the successive year.
(iv) The difference between the amount due at the end of two consecutive years = Simple interest for one year on the lesser amount.
(v) When the interest is payable half yearly divide the rate by 2 and multiply the time by 2.
When the interest is payable quarterly divide the rate by 4 and multiply the time by 4.
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