Interest rate kaise nikale? jab interest, principle aur time diya ho

Interest rate matlab, byaaj ki dar (ब्याज की दर) kaise nikale? Jab interest, principal aur time diya ho. Hello friend !! Simple interest aur principal kaise calculate karte hai? Matlab Ye dono ko kaise nikalte hai? Ye sab hum aapne last part me sikh chuke hai. Agar aap abhi tak nahi sikhe aur aap bhi inn dono ko sikhana chahte hai to iss topic ke end me humne link diya hai. Aap waha se sikh sakte hai.
Aaj hum aapko sikhayenge ki, jab saadharan byaaj, muldhan aur samay diya ho to varshik byaaj ki dar kaise nikalte hai ?
Varshik byaaj ki dar ko kaise calculate ya nikalte hai ?

Ye jaanane se pahle hum thoda ye jaan lete hai ki ye hota kya hai ?

Interest rate kaise nikale? Jab interest, principal aur time diya ho.

 Interest rate kya hota hai ?
Interest rate ko hindi me byaaj ki dar (ब्याज की दर ) kahte hai. Generally interest rate, varshik ( annual ) hota hai.
Jab hum kisi bank me kuch rupaye jama karte hai to iss jama kiye rupaye ko hum muldhan kahte hai aur per ₹100 muldhan par per year di jaane waali extra rupaye ko byaaj ki dar (Rate of interest) kahte hai. Matlab jab hum bank se apne rupaye nikalne jaayenge tab bank hume muldhan ke alawa kuch rupaye adhik dega. Ye adhik rupaye muldhan par ek fixed rate se diya jata hai.
Ab baat aati hai ki , issko calculate kaise karte hai? Issko calculate karne ke liye hum sabse pahle interest rate calculate karne ka formula banayene . Aayiye issko bhi sikhh lete hai.

 Interest Rate nikalane ka formula :

Interest Rate ka formula ko hum simple interest formula ki help se nikal sakte hai. Jiss prakar se last part me humne principal calculate karne ka formula banaya tha. Ussi prakar se hum interest rate ka bhi formula step-by-step banayenge.

 Step-1. Sabse pahle hum simple interest means saadharan byaaj ka formula lenge. Jo iss prakar se niche diya gaya hai:

Simple Interest =   principal×Rate×time  
                                               100

 Step-2. Ab uppar diye formula me cross (×) multiply karna hai.
Matlab L.H.S ke "ansh" ka multiply R.H.S. ke "har" se phir "equal to" likhna hai uske baad R.H.S ke "ansh" ka multiply L.H.S. ke "har" se karna hai.
Hum simple interest ko "interest" likh rahe hai.
interest×100 = principal×Rate×time 

 Step-3. Ab Hume "Rate" ka formula banana hai isliye hum R.H.S. se principal×time ko L.H.S me laayenge. Aap dekh sakte hai ki, principal×time , Rate ke saath multiply kiya hai. Islye jab isko L.H.S me laayenge tab ye interest×100 se divide kar lega.

Rate =     interest×100    

              principal×time

Yahi interest Rate nikalane ka formula hai. Issi formula se hum byaaj ki dar gyaat kar sakte hai.
Aayiye issi formula ka use karke questions ko solve karna sikh lete hai.

 Interest Rate calculate karne se related questions :

Ab hum isske kuch example question ko solve karna sikhte hai. Aap bhi ek pen and paper lekar humare saath-saath question ko solve karne ki practice kariye.

#Q-1. Yadi interest ₹50 principal ₹200 aur time 2 years ho to interest rate batayiye.

Solution-: Diya hai: Interest = ₹400, principal = ₹200 aur Time = 2 years

Isliye Rate =     interest×100    

                          principal×time
                     =    50×100   
                            200×2
                     = 12.5
Isliye Rate = 12.5%  Ans.

#Q-2. Yadi saadharan byaaj = ₹50, muldhan = ₹800 aur samay = 1 year ho to varshik byaaj ki dar gyaat kijiye.

Solution-: Diya hai: saadharan byaaj (SI) = ₹50, muldhan (p) = ₹800 aur samay (T) = 1 year
Isliye varshik byaaj ki dar = 
  Saadharan byaaj ×100   
  muldhan × samay
=   50×100  
      800×1
= 50/8
= 6.25
Isliye varshik byaaj ki dar = 6.25% Ans.

#Q-3. Yadi 4 years ka muldhan aur saadharan byaaj barabar (equal) ho to byaaj ki dar gyaat kijiye.

Solution-: Suppose karte hai ki, muldhan = p, saadharan byaaj = I aur byaaj ki dar = R . Diya hai : time = 4 years.
Lekin quation ke anusar: P = I
Isliye varshik byaaj ki dar = 
  Saadharan byaaj ×100   
  muldhan × time
R =   P×100 
          P×4
R = 100/4
R = 25
Isliye byaaj ki dar = 25%   Ans.

#Q-4. Annum interest rate kya hoga jab 6 years me amount , principal ka 2 guna hoga.

Solution-: suppose principal = P, Rate = R aur Time = 6 years
Tab SI = P×R×6/100 = 3PR/50
Isliye Amount = P+SI = P+(3PR/50)
                            = P(1+3R/50)
But according to the question,
P(1+3R/50) = 2P 
⇒1+3R/50 = 2
⇒ 3R/50 = 2-1
⇒ 3R/50 = 1
⇒ 3R = 50
⇒ R = 50/3
⇒ R = 16.67
Isliye annum interest Rate = 16.67%     Ans.


#Q-5. Interest rate gyaat kijiye yadi principal ₹1000, time 5 years aur amount ₹1360 ho.

Solution-: Diya hai: P = ₹1000, aur T = 5 years. Suppose karte hai ki, Rate = R , Tab SI = P×R×T/100
                     = 1000×R×5/100
                     = 50R

Amount = P+SI
1360 = 1000+50R
⇒ 50R = 1360-1000
⇒ 50R = 360
⇒ 5R = 36
⇒ R = 36/5 = 7.2
Isliye Interest Rate = 7.2%     Ans.
#Q-6. Varshik byaaj ki dar gyaat kijiye yadi muldhan= ₹500, samay = 2 years aur mishradhan = ₹560 ho.

Solution-: Diya hai: muldhan = 500 aur time = 2 years. Maana varshik byaaj ki dar = R, Tab saadharan byaaj SI = 500×R×2/100
                = 10R
Diya hai mishradhan = 560, isliye
Mishradhan = muldhan+byaaj
⇒ 560 = 500+10R
⇒ 560-500 = 10R
⇒ 60 = 10R
⇒ R = 60/10 = 6
Isliye Varshik byaaj ki dar = 6%   Ans.

#Q-7. Kis varshik byaaj ki dar se 5 years me kisi dhan (rupye) ka mishradhan 3 guna ho jaayega?

Solution-: Suppose karte hai ki muldhan = P, varshik byaaj ki dar = R aur time = 5 years. Isliye saadharan byaaj SI = P×R×5/100
                                    = PR/20
Isliye mishradhan = P+PR/20
                                   = P(1+R/20)
Ab question ke anusar,
P(1+R/20) = 3P 
⇒ 1+R/20 = 3
⇒ R/20 = 3-1
⇒ R/20 = 2
⇒ R = 40
Isliye 40% varshik byaaj ki dar se kisi dhan (rupaye) ka mishradhan 3 guna ho jaayega.

#Q-8. Kis interest rate se 15 years me kisi dhan (money) ka amount 4 guna ho jaayega?

Solution-: Suppose karte hai ki principal = P, interest Rate = R aur time = 15 years. Isliye simple interest SI = P×R×15/100
                    = 3PR/20
Isliye amount = P+3PR/20
                           = P(1+3R/20)
Ab question ke anusar,
P(1+3R/20) = 4P 
⇒ 1+3R/20 = 4
⇒ 3R/20 = 4-1
⇒ 3R/20 = 3
⇒ R = 60/3 = 20
Isliye 20% interest rate se kisi dhan (rupaye) ka amount 4 guna ho jaayega.

#Q-9. Yadi kisi dhan (money) ka interest, ek fixed interest rate se 5 years me uss dhan ka 8/5 ho jata hai to annum rate bataye.

Solution-: suppose karte hai ki, principal = P , Rate = R aur Time = 5 years.
Isliye simple interest (SI) = P×R×5/100
= PR/20

Ab according to the question : interest , principal ka 8/5 hoga isliye-:
⇒ 8p/5 = PR/20
⇒ 8/5 = R/20
⇒ R = 20×8/5
⇒ R = 32
Isliye annum rate = 32%       Ans.


#Q-10. Yadi interest aur principal ka anupat 3 years me 3:8 ho to Interest rate kya hoga? 

Solution-: Suppose karte hai ki principal = P, interest Rate = R aur Interest = I
Isliye I = P×R×3/100 = 3PR/100   .....(i)
Ab question ke anusar:
⇒ I:P = 3:8
⇒ I/P = 3/8
⇒ I = 3P/8   ........(ii)
Ab (i) aur (ii) ko equal rakhne par:
⇒ 3P/8 = 3PR/100
⇒ 3/8 = 3R/100
⇒ 1/8 = R/100
⇒ 8R = 100
⇒ R = 100/8 = 12.5
Isliye, Interest rate = 12.5%      Ans.
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