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The compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is:a) 1260b) 1261c) 1271d) 1281Answer 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, $\begin{align} & C.I.=8000{{\left( 1+\dfrac{20}{100\left( 4 \right)} \right)}^{4\times \dfrac{9}{12}}}-8000 \\ & C.I.=8000{{\left( 1+(0.25\times 0.2) \right)}^{3}}-8000 \\ & C.I.=8000{{\left( 1+.05 \right)}^{3}}-8000 \\ & C.I.=9261-8000 \\ & C.I.=1261 \\ \end{align}$ 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:
Correct Answer: Description for Correct answer: Rate %=20 % Time= 9 months When interest is being compounded quaterly Time=\( \Large \frac{9}{12} \times 4=3 \) Rate =\( \Large \frac{20}{4} \%=5 \%=\frac{1}{20} \) According to the question, 8000 units = Rs. 16000 1 unit = Rs. 2 1261 units = Rs.\( \Large 2 \times 1261\) = Rs. 2522 Part of solved Simple and compound interest questions and answers : >> Aptitude >> Simple and compound interest Q. The compound interest on 16000 Rs. for 9 months at 20% per annum, interest being compounded quarterly, is: NAVNEET KUMAR SABRE 6 years AGO GIVEN P=16000, R=20%, N=9MONTHS=3/4YEARS AND COMPOUNDED QUATERLY. FOR COMPOUNDED QUATERLY C.I.=AMOUNT - PRINCIPAL Simply putting the formula n getting the result. 20% per annum, so for quaterly its gonna be Given:P=Rs.16000,n=9months=3/4yrs,R=20%pa option 9) Like? Yes (11) | No (4) pugazh gandhi 6 years AGOformula for compound interest is P=Rs16000, R=20% per anum = 5% per quarter 1st quarter 800 according to question when interest is compounded Quarterly formula is given as therefore Amount=16000*[1+{20/4*100}]^3=18522 Since 9 months = 3/4 years since it is quarterly, first change the time and rate of its quarter parts. where as, for quarter time = 9 months which has 3 quarters rate=(20/4) = 5% now applying in compound interest formula CI=P(1+r/100)^n compound interest=16000{[(1+20/400)^(3*4/4)]-1} p=16000,t=9 months=3 quaters. A=P(1+r/n)^n×t Here P=16000,r=0.2,n=4,t=3/4 p=16000,R=20%=5% quaterly t=9months=3 quaters A=P*(1+(R/100)^N r=20/4= 5 n=3 p[1+(r/4)/100]^4n (16000 * (1 + 5/100) ^ 3) - 16000 = 2522. principal=16000/- Amount=16000*(1+(20/4)/100)^(9*3)/12 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, To find compound interest firstly we have to find amount i.e. 'A' then Compound Interest i.e. C.I For First 3 month 5% = 800 9 months= 3 quaters,so CI=16000*(1+(20/400))^4*(9/12) Amount(A)=P*(1+R/4/100)^4*n=18522 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 AGOhere principal p =16000; P=16000 1) first three month intrest 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. if we calculate C.I quarterly then we use Amount=16000(1+20/4*100)^3 amount=p[1+(r/4)/100]^4n p=16000 for compound interest calculated quaternerly Quarterly, so R=20/4=5% Compound Interest= Amount*(1+20/100)^3-1 sum=16000(1+[0.2/4])^0.75*4 CI= p*(1+r/100)^n - p; Amont=16000*(1+(20/40/1000^4*9/12 p=16000 compound interest = 16000×(21/20)^3= 18522 f=16000x(1+(0.2/4))^(4x0.75)=18522 interest 20% per annum means (20/4)=5% quarterly, (per 3 month). 16000*{1+5/100)^3} Rate =20% per annum compounded annually i.e after every 3 months p = 16000 9 months = 3 quarters amount= p(1+r/400)^(4*n) c.i = amount - principal = 18522-16000=2522 Like? Yes | No (1) Ankit Kumar Maurya 6 years AGOcompounded quarterly so rate becomes 20/4=5% we will put this in the compound interest formula and get answer 2522 Like? Yes | No (1) gulshan 6 years AGOA=16000*{1+(20/4*100)}^9*4/12 p=16000 CI=Amount -Principle CI=16000(1+20/400)^(3/4)*4 - 16000 Compound Interest quarterly = P(1+((R/4)/100))^4n given principal=16000 r=20% n=9months per annum for quaterly a=p[1+(r/n)]^nt GIVEN:-Compounded quartly P = 16000/- the compound quarterly formula is p(1+(r/4)/100)^4n given p=16000 ,r=20% and n=9/12=.75 A=
p[ 1 + (r/4)/100]^4n C.I= A-p What is the compound interest on 16000 for 9 months at 20% per annum?The compound interest on Rs. 16000 for 9 months at `20%` p.a, compounded quarterly is Rs. 2522.
What is the compound interest on Rs 16000 at 20% per annum for 9 months compounded quarterly 3 points Rs 2255 Rs 2500 Rs 2000 Rs 2522?The compound interest on Rs. 16000 for 9 months at 20% p.a, compounded quarterly is Rs. 2522.
What is the compound interest on ₹ 20000 for 9 months at the rate of 4% per annum when interest is compounded quarterly?Amount after 9 months =20000×(1+5100)3=20000×2120×2120×2120=23152.5Total interest =23152.5−20000=3152.5.
What will be the compound interest of 16000?Detailed Solution
3360. ∴ Compound interest = 16000 × (21/100) = 3360.
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