चक्रवृद्धि ब्याज शार्ट ट्रिक्स Unlocking Compound Interest with Ease Expert Short Tricks Revealed

## Compound interest Short Tricks चक्रवृद्धि ब्याज शार्ट ट्रिक्स

Hello Friends, In this article we are going to share some most important ** short tricks of compound interest problems in Hindi** as well as English language. This post also contain some definitions, short tricks types and important questions. This is very useful for those students who want to crack various entrance examinations.

: interest formula compoundImportant Formula for Compound Interest | |

If principle = P , rate = r% per annul , time = t years, C.I.=compound interest, and amount = A, then:- | |

1 | A = P {1+(r/100)}^t |

2 | If the rate for first, second and third year is r1%, r2% and r3%, then A = P{1+(r1/100)} {1+(r2/100)} {1+(r3/100)} |

3 | C.I.= P {1+(r/100)}^t – P |

4 | C.I.= [P{1+(r1/100)} {1+(r2/100)} {1+(r3/100)}] – P |

5 | When time is in form of fractions, like 2(1/2) then A = [P {1+(r/100)}^2] x [1 + {(1/2 r)/100}] |

## Type and* Compound Interest Short tricks *1:- compound interest formula

**1** If any principle ‘P’ at the rate of r% in time ‘t’ become amount ‘A’, then

r = [{(A/P)^1/t}-1] x 100% **2** If any principle at r% per annul compound interest in time t1 become amount A1 and in time t2 becomes amount A2, then

r = [(A2/A1)^{(1/t2) – t1} – 1] x 100% **3** If any principle at r% per annul compound interest in time t becomes n times, then

r = [{n^(1/2)} – 1] x 100% **4** If any principle at r% per annul compound interest in time t1 becomes n1 times and in time t2 becomes n2 times, then

r = {(n2/n1)^(1/t2 – 1)} x 100% **5** If any principle ‘P’ at the rate of r% compound interest, after 2 years difference between simple interest and compound interest become ‘D’, then

r = {(D/P)^(1/2)} x 100%

**Example:-** At how much rate per annul interest of 1600 rs in 2 years, the compound interest become 164 rs ?\

** Type and Compound Interest Short trick 2:-** compound interest formula

- Any wealth given on compound interest becomes m times in t years, then time for becoming m^n=(t x n) years.
- Any wealth given on compound interest becomes m times in t years, then in (t x n) years that wealth become m^n of it.

**Example:-**Any wealth given on compound interest becomes twice in 5 years, then in how much years that wealth will becomes its 8 times?

*Type and Compound Interest Short tricks 3:-* compound interest formula

*Type and Compound Interest Short tricks 3:-*

*1* If simple interest of any wealth of 2 years is X rs and compound interest of 2 years is Y rs , rate of annul interest:- r = {(Y-X)/(X / 2)} x 100% = [{2(Y-X)} / X] x 100%

*1*

*2* If simple interest of any wealth of second years is X rs and compound interest of second years is Y rs , rate of annul interest:- r = {(Y-X) / X} x 100% *3* If simple interest of any wealth of 2 years is X rs and compound interest of 2 years is Y rs , then that wealth will be P = {(X/2)^2}/(Y-X)} or = {(X^2)/4(Y-X)} rs

*2*

*3*

*4* If simple interest of any wealth of second years is X rs and compound interest of second years is Y rs, then that wealth will be :- P = {(X^2) / (Y-X)} rs

*4*

**Example:-**On any wealth at fixed rate, simple interest of 2 years is 800 rs and compound interest is 820 rs , then what will be the rate of interest per annul?

Most Important Questions (Asked in previous Exam) | |

Q1 | If Rs. 500 amounts to Rs. 583.20 in two years compounded annually, find the rate of interest per annum. यदि 500rs मूलधन जो 2 साल बाद चकरवरधी पर इयर 583.20rs हो जाता है। दर ज्ञात करो। |

Ans | Principal = Re. 500; Amount = Rs. 583.20; Time = 2 years. Let the rate be R% per annum. Then, [500(1+ R/100) ^2] = 583.20 or (1+R/100)^2 = 5832/5000 = 11664/0000 = (108/100) ^2 (1+R/100) ^2 = (108/100) ^2 1+R/100 = 108/100 R = 8 rate = 8% p.a. |

Q2 | If the compound interest on a certain sum at 16 2/3% for 3 years is Rs. 1270, find the simple interest on the same sum at the same rate and for the same period. यदि चक्र व्रधी ब्याज 1270rs हो जाता है 16 2/3% की दर से 3 साल मे। उनका सिम्पल इंटरेस्ट (सामान्य ब्याज) ज्ञात करो उसी दर और उसी समय के लिए । |

Ans | Let the sum be Re. x. Then, C.I = [x X {(1+50/(3×100)} ^3-x] = (343x/216 -x) = 127x/216 127x/216= 1270 or x = 1270×216/127 = 2160. Thus, the sum is Re. 2160. S.I. = Re. (2160 x50/3x 3 x 1/100) = Rs. 1080. |

Q3 | Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of Baiter 9 years, the interest being compounded at 4% per annum. A व B मे 1301 rs को विभाजित करो। जिस्से 7 साल बाद A का अमौंट B के 9 वर्ष बाद के अमौंट के बराबर हो जाता है। चक्र व्रधी ब्याज 4% की दर से है। |

Ans | Let the two parts be Rs. x and Rs. (1301 — x). x (1+4/100) ^7 = (1301-x) (1+4/100) ^9 x/(1301-x) = (1+4/100) ^2 = (26×26/25×25) 625x = 676 (1301 — x) = 1301x = 676 x 1301 x = 676. So, the two parts are Rs. 676 and Rs. (1301 — 676) i.e. Rs. 676 and R8. 625. |

Q4 | A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 5 years. Find the sum and rate percent. यदि मूलधन 7350rs 2 साल और 8575rs 5 साल मे हो जाते है। मूलधन और दर ज्ञात करो। |

Ans | S.I. on Rs. 7350 for 1 year = Rs. (8575 — 7350) = Rs. 1225. Rate (100×1225/7350×1) % = 16 2/3%. Let the sum be Rs. x Then, X(1+50/3×100) ^2 = 7350 Xx7/6×7/6 = X = (7350 x 36/49) = 5400. Sum = Rs. 5400. |

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*Type and Compound Interest Short tricks 4:-* interest formula compound

*Type and Compound Interest Short tricks 4:-*

If any wealth at fixed rate of compound interest in t years become X rs and in 2t years become Y rs , then that wealth = {(X^2) / Y }rs

**Example:-**If any wealth at fixed rate of compound interest in 3 years become 4500 rs and in 6 years become 13500 rs , then find that wealth?

*Type and Compound Interest Short trick 5:-* si and ci formula

*Type and Compound Interest Short trick 5:-*

#### If on any wealth the simple interest is X rs and on same wealth at any rate in any time compound interest is Y rs , then:- *1* Y = X {1 + (r/200)} *2* X = Y / {1 + (r/200)}

*1*

*2*

**Example:-** On any wealth at the rate is 10% per annul in 2 years simple interest is 4000 rs. On same wealth at any rate in any time how much will be compound interest?

*Type and Compound Interest Short trick 6: –* compound interest formula with example

*Type and Compound Interest Short trick 6: –*

#### If any wealth at rate r% of simple interest in 2 years become X rs and same wealth on compound interest at any rate in any time becomes Y rs, then:- *1* Y = X x [1+ {(r/10)^2} / (100 + 2r)] *2* X = Y / [1+ {(r/10)^2} / (100 + 2r)]

*1*

*2*

**Example:-** If any wealth at rate 10% of simple interest in 2 years become 2400 rs , then same wealth on compound interest at any rate in any time will become how much?

*Type and Compound Interest Short trick 7: –* compound interest formula with example

*Type and Compound Interest Short trick 7: –*

#### If amount of X rs at the rate r% of compound interest in 2 years become Y rs , then:- *1* Y = [X x {100 + 2r + (r^2 / 100)}] / 100 *2* X = (Y x 100) / {100 + 2r + (r^2 /100)}

*1*

*2*

**Example:-** How much will be the Amount of 5000 rs at the rate of 5% per annul compound interest in 2 years?

*Type and Compound Interest Short trick *8:- si and ci formula

- On any sum ‘P’ in 2 years at the rate of r% per annul, the difference between compond interest and simple interest is = (Pr^2) / (100^2)
- On any sum ‘P’ in 3 years at the rate of r% per annul, the difference between compond interest and simple interest is = Pr^2(300+r) / (100^3)

**Example:-** What will be difference between compound interest and simple interest on 50000 rs at the rate 4% per annul in 3 years?

## Type and Compound Interest Short trick 9:- si and ci formula

#### If compound interest of any wealth of second year is X rs then that wealth will be:- ‘P’ = X x 100 / {1 + (r/100)} Example:- What will be the principle of which compound interest of second year is 660 rs at the rate of 10% per annul?

Type and Compound Interest Short trick 10: – | |

1 | If credit of X rs at the rate of r% per year has to be paid in two equal installment of Y rs , then:- X = [Y / {1 + r/100}] + [Y / {1 + r/100}^2] |

2 | If credit of X rs at the rate of r% per year has to be paid in two equal installment of Y rs , then:- X = [Y / {1 + r/100}] + [Y / {1 + r/100}^2] + [Y / {1 + r/100}^3] |

**Example:-**If any credit of 441 rs is paid in two yearly installments. If rate of compound interest is 5% , how much wealth has credit?

## Type and Compound Interest Short trick 11: – compound interest formula with example

#### If compound interest of X rs at the rate of r% in two years is Y rs , then:- 1 Y = [X x {2r + (r^2/100)}] / 100 rs 2 X = Y x 100 / {2r + (r^2/100) rs Example:- what will be the compound interest on 1000 rs at the rate of 8% per annul compound interest in 2 years

interest formula compoundType and Compound Interest Short trick 12: – | |

If compound interest of X rs at the rate of r% in 3 years is Y rs , then:- | |

1 | Y = X x[3r + {r^2(300+r)} / (100^2)] / 100 rs |

2 | X = Y x 100 / [3r + {r^2(300+r)} / (100^2)] rs |

**Example:-** What will be the compound interest of 16000 rs at the rate of 1x(1/2) per year , wheres as the interest will charged per monthly ?