Simple and Compound interest formulas, shortcuts, tricks and solved examples:
If P =
Principal, A = Amount, R = Rate percent per year, T = T years, S.I = Simple
interest, C.I = Compound interest, Then,
1. For Simple interest:
(A). S.I =
(P × R × T)/100
(B) A = P +
S.I
2. For Compound interest:
(A) When
interest is compounded yearly,
(B) When interest is compounded half-yearly,
(C) When
interest is compounded quarterly
(D) When
time is in fraction of a year, say 2⅕
(E) If rate
of interest in 1st year, 2nd year …………..… nth year are R1%, R2%
…………. Rn% respectively, then,
3. Equivalent or Successive interest:
Single
equivalent interest rate or Successive interest rate of 20% and 10% is
Single
equivalent interest rate or Successive interest rate of 10%, 20% and 30% would
be
Since,
equivalent interest 10% and 20% is 28%
So,
equivalent interest of 28% and 30% will be,
Example: 01
A sum of Rs. 15,500 is lent out into two
parts, one at 8% and another one at 6%. If the total annual income is Rs. 1060,
the money lent at 8% is:
Solution:
Let the
money lent at 8% be Rs. x, then
[(x × 8 ×
1)/100] + [15500 - x) × 6 × 1/100] = 1060
or, 2x +
93000 = 106000
or, x = 6500
Therefore, the
money lent at 8% is Rs. 6500
Example: 02
A sum of money at compound interest amounts
to Rs. 10,580 in 2 years and to Rs. 12,176 in 3 years. The rate of interest per
annum is:
Solution:
Interest on
Rs. 10580 for 1 year = Rs. (12176 - 10580) = Rs. 1587
∴ Rate = [(100 × 1587)/10580]% = 15%
Hence, the
rate of interest per annum is 15%.
Example: 03
A sum of money becomes Rs. 13,380 after
3 years and Rs. 20,070 after 6 years on compound interest. The sum is:
Solution:
Let, the sum
be x, then
x[1 + (R/100)]3 =
13380 and, x[1 + (R/100)]6 = 20070
On dividing,
we get, [1 + (R/100)]3 = (20070/13380) = 3/2
∴ x (3/2) = 13380
or, x = 13380 × (3/2)
= 8920
Hence, the
sum is Rs. 8920.Simple and Compound Interest Next Tests: