The compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is: a) 1260 b) 1261 c) 1271 d) 1281
Answer
Verified
Hint: Use the formula of compound interest $C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$, where P is the principal (or original amount), r is the annual rate, n is the number of times interest compounded per time period, t is the number of years on which interest has applied.
Complete step-by-step answer:
We are going to use the formula of compound interest which is written below:
$C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$
Where P: the Principal (or original
amount)
r: annual rate of interest
n: number of times interest compounded per time period
t: number of years on which the interest has applied
It is given that:
The principal (or original amount) is Rs 8000.
Annual rate of interest is 20%.
The interest is compounding quarterly means n = 4.
The interest compounded quarterly for 9 months means $t=\dfrac{9}{12}$year.
Now, substituting these values in the compound interest formula we get,
So, the compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is 1261.
Hence, the correct option is (b).
Note:
While applying the formula of compound interest there are some common mistakes that could happen: When substituting the value of r, don’t forget to divide the rate by 100. There could be confusion with the “compounded quarterly” statement, it means in a year interest is 4 times compounded so n value will be 4. And the “t” should be in years if in the question “t” is not given in years first convert it into years then apply in the formula.
True
Explanation;
Hint:
Principal (P) = 16000
n = 9 months = `9/12` years
r = 20% p.a
For compounding quarterly, we have to use below formula,
Amount (A) = `"P" xx (1 + "r"/100)^(4"n")`
Since quarterly we have to divide ‘r’ by 4
r = `20/4` = 5%
A = `1600(1 + 5/100)^(9/12 xx 4)`
= `16000(105/100)^(9/12 xx 4)`
= `16000(105/100)^(9/3)`
= `16000
xx (21/20)^3`
= `16000 xx 21/20 xx 21/20 xx 21/20`
= 18522
∴ Interest A – P = 18522 – 16000 = 2522
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 :)
Like? Yes (36) | No (8)Dinesh kumar sah 6 years AGO
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.
Like? Yes (20) | No (4)Ankit Sharma 6 years AGO
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
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)
Like? Yes (8) | No (3)G.S.Kantharao 6 years AGO
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
Like? Yes (12) |
No (7)Devireddy Jashuva 6 years AGO
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
Like? Yes (1) |
No sujit sinha 6 years AGO
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
Like? Yes (1) | No shivani shukla 6 years AGO
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
Like? Yes (1) | No (1)rohith sundaresan 6
years AGO
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)
Like? Yes (1) | No (1)Dipanjan Mukherjee 6 years AGO
9 months= 3 quaters,so rate =20%=r/4= 5% per quater Ci=16000(1+5/100)^3-16000=2522
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.
Like? Yes | No shaik jasmin 6 years AGO
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
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
Like? Yes (1) | No (1)muskan Khandelwal 6 years AGO
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
Like? Yes | No (1)prakash sharma 6 years AGO
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
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
Like? Yes | No (1)A.KARTHIKA 6 years AGO
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
Like? Yes | No (1)bagyalakshmi 6 years AGO
Compound Interest= Amount*(1+20/100)^3-1 So, C.I=16000*(1+20/100)3-1 C.I=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;
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
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
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
Like? Yes |
No (1)gulshan 6 years AGO
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
Like? Yes | No (1)harshit agarwal 6 years AGO
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
Like? Yes | No (1)Karan Saxena 6 years AGO
CI=Amount -Principle
CI=16000(1+20/400)^(3/4)*4 - 16000 so answer will be 2522
Like? Yes (1) | No (2)
ANUSHKA BAJPAI 6 years AGO
Compound Interest quarterly = P(1+((R/4)/100))^4n where, P is principal R is rate of
Interest N is time (in years )
Like? Yes (1) | No (2)Manisha gouri 6 years AGO
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
Like? Yes | No (1)Samruddha 6 years AGO
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
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/-
Like? Yes | No (1)phanikumar 6 years AGO
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