Simple and Compound interest Aptitude formulas

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% …………. 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,

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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.

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Simple and Compound Interest:
Formula:                Simple and Compound Interest Formulas
Solved Examples:  Solved Examples: Set 01
Practice Test:         Practice Test: 01     Practice Test: 02     Practice Test: 03
                                 Practice Test: 04     Practice Test: 05     Practice Test: 06