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__Simple and Compound interest formulas, shortcuts, tricks and solved examples__:

__Simple and Compound interest formulas, shortcuts, tricks and solved examples__:

**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 R

_{1}%, R_{2}% …………. R_{n}% 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:**