Friday, 12 August 2016

चक्रवृद्धि ब्याज: Short Tricks of Compound Interest In Hindi | शार्ट ट्रिक्स कंपाउंड इंटरेस्ट चक्रवृद्धि ब्याज Objectives Old Papers

Compound interest 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. 

Important 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}]




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:-
  1. Any wealth given on compound interest becomes m times in t years, then time for becoming m^n=(t x n) years.
  2. 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 trick 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%
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
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


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/(3x100)} ^3-x]
= (343x/216 -x) = 127x/216
127x/216= 1270 or x = 1270x216/127 = 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 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 = (26x26/25x25)
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 (100x1225/7350x1) % = 16 2/3%.
Let the sum be Rs. x Then,
X(1+50/3x100) ^2 = 7350
Xx7/6x7/6 =
X = (7350 x 36/49) = 5400.
Sum = Rs. 5400.

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>> Maths Short Tricks in Hindi  <<




Type and Compound Interest Short trick 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:-
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)}


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: -
 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)]

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: -
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)}

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:-

  1. 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)
  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:-

               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: -

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 










Type 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 ?


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Questions asked in exams of Compound Interest

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