Find the compound interest on Rs 16000 at 20% per annum for 1 year when compounded quarterly

NAVNEET KUMAR SABRE   6 years AGO

GIVEN P=16000, R=20%, N=9MONTHS=3/4YEARS AND COMPOUNDED QUATERLY.

FOR COMPOUNDED QUATERLY
AMOUNT = P[1+(R/4)/100]^4N
=16000[1+(20/4)/100]^{4 X (3/4) }
=16 X (21/20)^3
=18522
COMPOUND INTEREST (C.I.) IS

C.I.=AMOUNT - PRINCIPAL
=18522-16000
=Rs 2522............answer :)

Simply putting the formula n getting the result.
p=16000,r=20? but when compounded quarterly then rate will become 1/4th of the yearly ie 5? and time period will become 4 times of the original time period ie t=9�4 months=36 months=3 years.then CI=?
CI=p{[1+(r/100)]^n-1}
=16000{[1+(5/100)]^3-1}
=2522 Ans
Hence option (9) is the right answer.

20% per annum, so for quaterly its gonna be
20/4=5%
so total amount= 16000(1+5/100)^3
= 18522
hence CI=18522-16000
= 2522
so answer is option (9) 2522

Given:P=Rs.16000,n=9months=3/4yrs,R=20%pa
Amount=P(1+R/4*100)^4n
=16000(1+20/400)^3/4*4
=16000(1+5/100)^3
=16000*21/20*21/20*21/20
=Rs.18522
Compound Interest =>18522-16000
=>Rs.2522

option 9)

formula for compound interest is
SUM=PRINCIPAL*[1+(r/n)]^nt
n=compounded period
t=no. of years
r=rate of intrest/100
16000[1+(0.2/4)]^0.75*4 = 18522
interest = 18522-16000
=2522
so correct opt is 9)

P=Rs16000, R=20% per anum = 5% per quarter
Time=9months=3quarters
Compound Intrest= P{1+(R/100)}^n - P
= 16000(1+0.5)^3 -16000= 2522

1st quarter 800
2nd quarter 800+40
3rd quarter 800+82
total=2522

according to question

when interest is compounded Quarterly formula is given as
Amount=P[1+{(R/4)/100}]^4*n
time = 9 months ==> 4 quarters=4*9 =36 months=3 years .

therefore Amount=16000*[1+{20/4*100}]^3=18522
compound interest=18522-16000=Rs.2522.

Since 9 months = 3/4 years
So, C.I = (16000*(1+((20/4)/100))^3)-16000 = 2522
Hence, option 9 is correct ans.

since it is quarterly, first change the time and rate of its quarter parts.

where as,
time= 9months =9/12 yr
rate=20%

for quarter

time = 9 months which has 3 quarters
so time=3

rate=(20/4) = 5%

now applying in compound interest formula

CI=P(1+r/100)^n
CI=16000*(1+5/100)^3
CI=2522

compound interest=16000{[(1+20/400)^(3*4/4)]-1}
CI=18522-16000
CI=2522
so the correct answer is option 9) 2522

p=16000,t=9 months=3 quaters.
r=20% annum =5% quarter
amt = (16000*(1+5/100)3)
=18522
c.i = 18522-16000 = 2522

A=P(1+r/n)^n×t Here P=16000,r=0.2,n=4,t=3/4
CI=A-P

p=16000,R=20%=5% quaterly t=9months=3 quaters
amount=p(1+(r/4/100)power of 3
16000*(1+5/100)power of 3
=16000*21/20*21/20*21/20=18522
C.I=18522-16000=2522

A=P*(1+(R/100)^N
P=16000
RATE=20%,IT WILL BE 20/4=5%
TIME=9 MONTH=3 QUARTERS
HENCE,
A=16000(1+(5/100)^3
=18522
THEN
C.I=A-P
=18522-16000
=2522

r=20/4= 5 n=3
16000(1+5/100)^3=18522
18522-16000=2522

p[1+(r/4)/100]^4n
16000[1+(20/4)/100]^3
=18522
ci=18522-16000
=2522

(16000 * (1 + 5/100) ^ 3) - 16000 = 2522.
As Quarterly compounded so rate will be (20/4) i.e 5 % and time of 9 months will be 3 periods of 3 months .

principal=16000/-
time=9months=3quarters
rate=20%per annum=5% per quarter
amount=16000*(1+(5/100))^3=16000*(21/20)^3=18522
C.I=18522-16000=2522

Amount=16000*(1+(20/4)/100)^(9*3)/12
=>16000(105/100)^3
=>18522
CI=18522-16000
CI=2522

here r=20/4=5% because interest is calculated quarterly then given n=9 months which has 3 quarter parts a year so n=3 then use it in the compound interest formula

As it is compounded quarterly,
so rate =20/4%=5%
Time=(9/12)*4=3
Amount=16000(1+5/100)^3
=18,522
so C.I.=18,522-16,000
=2522

To find compound interest firstly we have to find amount i.e. 'A' then Compound Interest i.e. C.I
as we have to find C.I quarterly so we will put all the values in the formula i.e. A=P(1+(R/4)/100)^4n
where p=16000
time=9 month=3 quaters
rate=R=20%,it will be 20/4=5%
hence,
A=16000(1+5/100)^3
=18522
then C.I=A-P
=18522-16000
=2522

For First 3 month 5% = 800
Second 3 months 5%= 800+ 5% 800
Third 3 months 5%= 840+ 5% 840
Total = 800+(800+40)+(840+42)

9 months= 3 quaters,so
rate =20%=r/4= 5% per quater
Ci=16000(1+5/100)^3-16000=2522

CI=16000*(1+(20/400))^4*(9/12)
CI=18522
therefore compound interst=18522-16000=2522

Amount(A)=P*(1+R/4/100)^4*n=18522
CI=18522-16000=2522
Option 9)

4 quarter in one year so 5% quarterly and intrest for 3 more quarter.now simple compound intrest rate 5% time 3 quarter and amount 16000.

here principal p =16000;
time t =9 months=9/12 years;
rate r=20%;
amount=p[1+((r/4)/100)]^4t
=16000[1+((20/4)/100)]^[4*(9/12)]
=18522
ci=amount-principal
=18522-16000
=2522

P=16000
T=9 month= 3 quarter
R=20%, 20/4=5%
A=P(1+R/100)^T
=18522
INTEREST=18522-16000=2522

1) first three month intrest
(16000*20*0.25)/100 =800
after 3 month principal amount is 16800
then intrest after next 3 months = 840
after 6 months principal amount become 17640
after 9 months amount become 18522
so intrest is 18522-16000 = 2522

As it is quarterly compounded...so rate will be 1/4 n time will be 4 Times of the given one I.e. R=5% and T=3 years.
c.i. = P*(100+R/100)^T

if we calculate C.I quarterly then we use
Interest=P{1+((r/4)/100)}^4n -p where p=capital
r=rate,n=year
so in this question
Interest = 16000[1+(20/5)/100]^(4*9/12)-16000
=>18522-16000=2522

Amount=16000(1+20/4*100)^3
=18522.
18522-16000=2522(option 9)

amount=p[1+(r/4)/100]^4n
9 months=9/12=3/4
16000[1+(20/4)/100]^4(3/4)
finally 16000(105/100)^3
=18522(amount)
therefore compund interest=amount-princlipal
18522-16000=2522

p=16000
r=20%
t=9 months
=9/12 year
=3/4
CI=16000(1+(20/4)/100)^4*(3/4)
=16000(21/20)^3
=18522
compound interest=18522-16000
=2522 (option 9)

for compound interest calculated quaternerly
amount A=p(1+((r/4)/100))^4n
where p =principal amount
r=rate per annum
n=no of years
hence we get total amount after 9 months as Rs 18522
to get the compound interest CI =A-P
=18522 -16000
=Rs 2522

Quarterly, so R=20/4=5%
there are 3 quarters in 9 months
:- c.i=16000((1+5/100)^3)-1)
=16000* 1261/ 8000
=2522
ans:- 9) 2522

Compound Interest= Amount*(1+20/100)^3-1
So, C.I=16000*(1+20/100)3-1
C.I=2522

sum=16000(1+[0.2/4])^0.75*4
=18522
int=18522-16000=2522

CI= p*(1+r/100)^n - p;
16000*(1+5/100)^3 - 16000
here Interest rate is 20% per annum for a quarter it would be 20/4;
since interest is added after each qaurter so n = 9months/12 *4;

Amont=16000*(1+(20/40/1000^4*9/12
A=18522
componded interest=18522-16000
=2522

p=16000
time=9month= 3 quarters.
amount=1600*(1+(5/100))^3=18522
c.i=amount-princi=18522-16000=2522

compound interest = 16000×(21/20)^3= 18522
so CI= 18522-16000- 2522

f=16000x(1+(0.2/4))^(4x0.75)=18522
ci= 18522-16000=2522

interest 20% per annum means (20/4)=5% quarterly, (per 3 month).
Now, Principal+Interest for 9 month on 16000= 16000(1+5/100)^3 = 2522.
The power 3 comes from 9/3=3, as interest is counting per 3 month

16000*{1+5/100)^3}
16000*{9261/8000}
18522
18522-16000
2522

Rate =20% per annum compounded annually i.e after every 3 months
so rate of interest every 3 month will be (20/4)% =5%
after 9 months amount will be
16000 [1 + {5/100}]^3=18522
Interest will be 18522-16000=2522 Rs
Hence answer will be option 9). 2522

p = 16000
r = 20

9 months = 3 quarters
n = 3/4

amount= p(1+r/400)^(4*n)
amount = 16000*(1 + 20/400)^3 = 18522

c.i = amount - principal = 18522-16000=2522

compounded quarterly so rate becomes 20/4=5%
and time become 9/3=3

we will put this in the compound interest formula and get answer 2522

A=16000*{1+(20/4*100)}^9*4/12
A=16000*{1+1/20}^3
A=16000*(21/20)^3
A=18522
CI=A - P
CI=18522-16000
= 2522

p=16000
t=9 months=3 quarters
r=20% per annum=5% per quarter
a=16000*(1+(5/100))^3
a=18522 interest=18522-16000=2522

CI=Amount -Principle

CI=16000(1+20/400)^(3/4)*4 - 16000
so answer will be 2522

Compound Interest quarterly = P(1+((R/4)/100))^4n
where,
P is principal
R is rate of Interest
N is time (in years )

given principal=16000 r=20% n=9months per annum for quaterly
now we should calculate first Amount
Amount = p(1+(r/4)/100)^4n
= 16000(1+(20/4)/100)^4*(9/12
Amount = 18522
now we need to calculate compound interest,formula is
compound interest =amount-principal
=18522-16000
C.I =2522

a=p[1+(r/n)]^nt
p=16000;r=20%=0.2;n=4;t=9/12 years
a=18522 ,now intrest=18522-16000=2522

GIVEN:-Compounded quartly
p=16000
r=20%
AMOUNT=P(1+(R/4)/100)^4N
A=18522
C.I=18522-16000=2522

P = 16000/-
R = 20% per annum = 5% per quarter.
T = 9 months = 9/12 yr
So,compounded quarterly ,4n here n is in year.Hence ,
T = (9/12)*4 = 3 .
Now,
A = P(1 + (R/4)/100) ^4n
A = 16000 (1 + 5/100) ^3
= 18522
compound Interest = Amount - Principle
=18522 - 16000
=2522/-

the compound quarterly formula is p(1+(r/4)/100)^4n

given p=16000 ,r=20% and n=9/12=.75
so finally wet ans 18522
so 18522-16000=2522 so ans is 2522

A= p[ 1 + (r/4)/100]^4n
A= 16000[ 1+ (20/5)/100]^ 4* 3/4
A= 16000[ 1+ (1/20)]^3
A= 16000[ (21/20)]^3
A= 18552

C.I= A-p
C.I= 18552- 16000
C.i = 2552

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