Compound Interest is a method of calculating interest whereby interest earned overtime is added to the principal.

OR, The interest is calculated on the amount of the previous year is known as compound interest or interest compound.

## Formula of Compound Interest :-

â€¢ When Interest is compounded Annually

A = P(1 + r/n)*nt where, A – final Amount.

P – Principal Balance

r – Interest Rate

n – no of Interest rate

T – Time period

OR.

A = P(1+ R/100)n , CI = A – P

â€¢ When Interest is Compounded Half- yearly

A = P{1 + (R/2)/100}*2n

â€¢ When Interest is Compounded quarterly

A= P{1+(R/4)/100}*4n

â€¢ When rates bare different for different year ,R1 for 1st year, R2 for 2nd year, R3 for 3rd year .

A = P(1+ R1/100)(1+ R2/100)(1+R3/100)

â€¢ If the rate of the growth is constant.

V= VÂ°(1+R/100)*n

â€¢ If the rate of the depreciation is constant

V = VÂ°(1-R/100)*n

â€¢ Population after n year

P = (1+R/100)*n

Compound Interest is an essential part of any Competitive exam like SSC, Railway, Banking, UPSC or PCS Exam . Any Competitive exam asked questions repeatedly from this topic . Compound interest is a section of Quantitative Aptitude.

Every year 1 – 2 questions have been asked in competitive exam from this topic. So, if you want to crack this topic you must practice this topic in proper way .

## Let see some examples of Compounds Interest:-

(1) Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly ?

Solution – Given,

P = 8000

R = 5%

T = 3years

A = 8000(1+5/100)*3

= 8000( 105/100)*3

= 8000 Ã— 105/100Ã—105/100 Ã— 105/100

= 8000 Ã— 21/20Ã—21/20 Ã— 21/20

= 9261

CI = A -P

= 8000 – 9261

= 1261.

(2) If Rs 7500 are borrowed at CI at the rate of 4% , per annum then after 2year the amount to be paid is ?

Solution- Given,

P = 7500

R = 4%

T = 2years

A= 7500(1 + 4/100)* 2

= 7500 Ã— 104/100 Ã— 104/100 Ã— 104/100

= 7500 Ã— 26/25 Ã— 26/25 Ã— 26/25

= 8112

(3) Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest she rent it to alam at the same rate but Compounded annually . find her gain after 2 years.

Solution – Given ,

P = 20000

R = 12%

T = 2years

SI = PÃ—RÃ—T/2

= 2000Ã—12Ã—2/200

= Rs 4800

In case of Alam,

Interest of the 1st year

SI = 20000Ã— 12Ã—1/100

= Rs 2400

Amount at the end if the first year,

Rs 20000 + Rs 2400 = Rs 22400

Interest for the 2nd year

SI = 22400Ã— 12Ã—1/100

= Rs 2688

CI for 2nd year , Rs 2400 + Rs 2688 = Rs 5088

Amount of gain = Rs 5088 – Rs 4800 = Rs 288 .

All the best for you exam .stay well, stay safe.

Also read – Boat and Stream pdf

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