This post is a collection of important compound interest multiple choice questions.
All the questions are important as they have been previously asked in competition exams like GRE, GMAT, Math Olympiad, SSC, CAT, NMAT, CMAT, SBI po etc.
My sincere request for all the students out there is to practice all the questions and try to remember the concept used for each question.
Compound Interest MCQ
Q1. A sum of money placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?
(a) 9 years (b) 8 years
(c) 27 years (c) 7 years
Read Solution
Sol1:\quad Let\quad the\quad Principal\quad be\quad P,\quad Time(n)=3,\quad { A }1=2P\\\ \\ Case\quad 1;\quad { A }1=P{ (1+\frac { R }{ 100 } ) }^{ n }\\ \\ 2P=P{ (1+\frac { R }{ 100 } ) }^{ 3 }………(a)\\\ \\ \\\ \\ Case\quad 2;\quad { A }2=8P,Time=t\\\ \\ { A }2=P{ (1+\frac { R }{ 100 } ) }^{ t }\\ \\ 8P=P{ (1+\frac { R }{ 100 } ) }^{ t }\\ \\ { (2P) }^{ 3 }=P{ (1+\frac { R }{ 100 } ) }^{ t }……(b)\\\ \\ \\\ \\ From\quad 'a'\quad and\quad 'b'\\\ \\ { [{ (1+\frac { R }{ 100 } ) }^{ 3 }] }^{ 3 }={ (1+\frac { R }{ 100 } ) }^{ t }\\ \\ { (1+\frac { R }{ 100 } ) }^{ 9 }={ (1+\frac { R }{ 100 } ) }^{ t }\\\ \\ Comparing\quad RHS\quad and\quad LHS,\quad we\quad get\\ \\ t=9\\\ \\ Hence,\quad in\quad 9\quad years\quad will\quad it\quad amount\quad to\quad 8\quad times\quad itself.
Hence (a) is the right answer
Q2. Divide 3903 between Rakesh Yadav and Bhuvnesh such that Rakesh share at the end of 7 years is equal to Bhuvnesh share at the end of 9 years at 4% per annum rate of compound interest.
(a) Rakesh=₹2028,
Bhuvnesh=₹1875
(b) Rakesh=₹2008,
Bhuvnesh=₹1000
(c) Rakesh=₹2902,
Bhuvnesh=₹1001
(d) Rakesh=₹2600,
Bhuvnesh=₹1303
Read Solution
Sol:\quad Case\quad 1:\quad For\quad Rakesh\\ \\ Rate(R)=4,\quad Time({ n }1)=7\\\ \\ \ { A }1=P{ (1+\frac { 4 }{ 100 } ) }^{ 7 }\\ \\ \ { A }1=P{ (\frac { 26 }{ 25 } ) }^{ 7 }………(a)\\\ \\ \\\ \\ \ Case2;\quad For\quad Bhuvnesh\\ \\ Rate(R)=4,\quad Time({ n }2)=9\\ \\ { A }1=P{ (1+\frac { R }{ 100 } ) }^{ { n }2 }\\ \\ { A }1=P{ (1+\frac { 4 }{ 100 } ) }^{ 9 }\\ \\ \ { A }1=P{ (\frac { 26 }{ 25 } ) }^{ 9 }………(b)\\\ \\ \\\ \\ Subtracting\quad equation\quad 'a'\quad from\quad equation\quad 'b'\\ \\ P{ (\frac { 26 }{ 25 } ) }^{ 9 }-P{ (\frac { 26 }{ 25 } ) }^{ 7 }\\ \\ P{ (\frac { 26 }{ 25 } ) }^{ 2 }\\ \\ P(\frac { 676 }{ 625 } )……..(c)\\\ \\ \\\ \\ from\quad equation\quad 'c'\quad we\quad get\quad Rakesh's\quad and\quad Bhuvnesh's\quad share,\quad that\quad is;\\ \\ Rakesh's\quad share=676x\\ \\ Bhuvnesh's\quad share=625x\\\ \\ Rakesh's\quad share+Bhuvnesh's\quad share=3903\\ \\ 676x+625x=3903\\ \\ 1301x=3903\\ \\ x=\frac { 3903 }{ 1301 } \\ \\ x=₹3\\\ \\ Share\quad of\quad Rakesh\quad =676\times 3=₹2028\\ \\ Share\quad of\quad Bhuvnesh=625\times 3=₹1875
option (a) is the right answer
Q3. If the simple Interest is 10.5% annual and compound interest is 10% annual, find the difference between the interests after 3 years on a sum of ₹1000.
(a) ₹15 (b) ₹12
(c) ₹16 (d) ₹11
Read Solution
Principal(P)=1000,\quad Time(T)=3years,\quad Rate\quad (R)=10.5,\quad Rate(r)=10\\\ \\ \quad \ \ Simple\quad Interest\quad for\quad 3\quad years=\frac { 1000\times 10.5\times 3 }{ 100 } \\ \\ Simple\quad Interest\quad for\quad 3\quad years=₹315\\\ \\ \\\ \\ Compound\quad Interest\quad for\quad 3\quad years=A-P\\ \\ Compound\quad Interest\quad for\quad 3\quad years=P{ (1+\frac { r }{ 100 } ) }^{ t }-P\\ \\ Compound\quad Interest\quad for\quad 3\quad years=1000{ (1+\frac { 10 }{ 100 } ) }^{ 3 }-1000\\ \\ \ Compound\quad Interest\quad for\quad 3\quad years=1331-1000\\ \\ Compound\quad Interest\quad for\quad 3\quad years=₹331\\\ \\ \\\ \\ Required\quad difference=331-315=₹16\\\ \\ Hence,\quad the\quad difference\quad between\quad C.I\quad and\quad S.I\quad is\quad ₹16
option (c) is the right answer
Q4.What will be the present value of payable ₹14580 after two years at 8% per annum compound interest?
(a) ₹11500 (b) ₹12500
(c) ₹10500 (d) None of these
Read Solution
\ \ \ \ \ \ \ \ Amount(A)=14580,\quad Rate(R)=8,\quad Time(n)=2\\\ \\ 14580=P{ (1+\frac { 8 }{ 100 } ) }^{ 2 }\\\ \\ 14580=P{ (\frac { 729 }{ 625 } ) }\\\ \\ \ P=₹12500\\\ \\ \ Present\quad value\quad is\quad ₹12500.\ \ \
option (b) is the right answer
Q5. What annual payment will discharge a debt of ₹1025 due in 2 years at the rate of 5% compound interest.
(a) ₹515.25 (b) ₹561.25
(c) ₹516.25 (d) ₹551.25
Read Solution
Principal(P)=1025,\quad Rate(R)=5,\quad Time(n)=2\\\ \\ Annual\quad Payment=\quad \frac { P }{ \frac { 1 }{ { (1+\frac { R }{ 100 } ) } } +\frac { 1 }{ { (1+\frac { R }{ 100 } ) }^{ 2 } } } \\\ \\ Annual\quad Payment=\quad \frac { 1025 }{ \frac { 1 }{ { (1+\frac { 5 }{ 100 } ) } } +\frac { 1 }{ { (1+\frac { 5 }{ 100 } ) }^{ 2 } } } \\\ \\ Annual\quad Payment=\quad 1025\times \frac { 441 }{ 820 } \\\ \\ Annual\quad Payment=\quad ₹551.25\
option (a) is the right answer
Q6. A tree increases ![]()
times per year in length. If present height of the tree is 64cm, then what will be the height after two years?
(a)72cm (b)90cm
(c)81cm (d) None of these
Read Solution
Principal(P)=64,\quad Rate(R)=\frac { 1 }{ 8 } \times 100=12.5,\quad Time(n)=2\\\ \\ A=P{ (1+\frac { R }{ 100 } ) }^{ n }\\\ \\ A=64{ (1+\frac { 12.5 }{ 100 } ) }^{ 2 }\\\ \\ A=81cm\\\ \\ Hence,\quad After\quad two\quad years\quad height\quad of\quad the\quad tree\quad will\quad be\quad 81cm
Option (c) is the right answer
Q07. A sum of ₹2400 deposited at CI, doubled after 5 year. After 20 years it will become:
(a) ₹24000 (b) ₹19200
(c) ₹38400 (d) can’t be determined
Read Solution
Let\quad the\quad Principal(P)=2400\\\ \\ According\quad to\quad question;\quad Sum\quad will\quad doubled\quad after\quad 5\quad years\\\ \\ Principal\qquad \quad Time\qquad \qquad Amount\qquad \\\\ \\ \quad \quad 2400\quad \qquad \quad \quad 5\qquad \qquad \qquad 4800\ \quad \\\ \\ \quad 2400\qquad \quad 5\times 4=20\qquad \quad 4800\times 4=19200\\\ \\ So,\quad After\quad 20\quad years\quad Sum\quad will\quad be\quad ₹19200.
Option (b) is the right answer
Q08. A certain sum amounts to ₹8988.8 in two year and to ₹9528.128 in three years, at compound interest per annum. What is the principal and rate of interest?
(a) ₹12000, 5% (b) ₹6000, 8%
(c) ₹8000, 6% (d) ₹10000, 8.5%
Read Solution
{ A }1=₹8988.8,\quad { A }2=₹9528.128,\quad n=2\\\ \\ \quad \ According\quad to\quad Question\\\ \\ \frac { { A }1 }{ { A }2 } =\frac { 8988.8 }{ 9528.128 } =\frac { 53 }{ 50 } \\\ \\ P={ A }1{ (\frac { { A }1 }{ { A }2 } ) }^{ 2 }\\\ \\ P=8988.8{ (\frac { 50 }{ 53 } ) }^{ 2 }\\\ \\ \ P=₹8000\\\ \\ \ Rate=(\frac { { A }2-{ A }1 }{ { A }1 } )\times 100\\\ \\ Rate=(\frac { 53-50 }{ 50 } )\times 100\\\ \\ Rate=\quad 6\\\ \\ Hence,\quad Principal\quad is\quad ₹8000\quad and\quad Rate\quad is\quad 6percent.
Option (c) is the right answer
