Q.To what amount will ₹12000 accumulate in 12 years if invested at an effective rate of 5%?

Showing the 12 most recent of 39 on this concept.

1. CA Foundation 2026Set jan-20261 markMCQ
   Q.If an amount is compounded annually so that it tripled itself in 4 years, then the annual rate of interest is (Given that $3^{1/4}=1.316$) (A) 13.6% (B) 31.1% (C) 31.6% (D) 11.3%

   ›Reveal solutionSolution

   $(1+r)^4=3\Rightarrow 1+r=3^{1/4}=1.316\Rightarrow r=31.6\%$.

   Step 1 — set up the compound-growth equation

   Tripling in 4 years: $P(1+r)^4=3P$, so

   $(1+r)^4=3.$

   Step 2 — take the fourth root

   $1+r=3^{1/4}=1.316.$

   Step 3 — extract the rate

   $r=1.316-1=0.316=31.6\%\text{ per annum}.$

   Watch out

   Remember to subtract 1 after taking the root. $3^{1/4}=1.316$ is the growth factor, not the rate — reading 13.6% (option A) by misplacing the digits, or forgetting the $-1$, are the built-in traps here. …

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2. CA Foundation 2026Set jan-20261 markMCQ
   Q.Bank B provides loans at 15% per annum compound interest. If Mr. XYZ borrowed ₹ 3,200 for 2 years from Bank B, then how much interest must Mr. XYZ pay to his bank? (A) ₹ 400 (B) ₹ 960 (C) ₹ 4,232 (D) ₹ 1,032

   ›Reveal solutionSolution

   $A=3200(1.15)^2=₹4,232$; interest $=4232-3200=₹1,032$.

   Step 1 — compound amount

   $A=P(1+r)^n=3200(1.15)^2.$

   Since $(1.15)^2=1.3225$:

   $A=3200\times 1.3225=₹4,232.$

   Step 2 — interest = amount − principal

   $CI=4232-3200=₹1,032.$

   Watch out

   Option (C) ₹4,232 is the total amount payable, not the interest. The question asks only for the interest, so you must subtract the principal — stopping at the amount is the most common trap on this question. …

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3. CA Foundation 2026Set jan-20261 markMCQ
   Q.If $₹\ 80,000$ grows to $₹\ x$ in 3 years at compound interest compounded annually at 8% rate of interest per annum, then the value of $x$ is: (A) ₹1,00,776.96 (B) ₹1,02,985.98 (C) ₹1,03,680.64 (D) ₹99,850.50

   ›Reveal solutionSolution

   $A=P(1+i)^n=80000\times(1.08)^3=₹1,00,776.96$.

   Step 1 — Formula

   For annual compounding, the maturity value is

   $A=P(1+i)^n.$

   Step 2 — Substitute

   With $P=₹80,000$, $i=8\%=0.08$, $n=3$:

   $A=80000\times(1.08)^3.$

   Step 3 — Evaluate the factor

   $(1.08)^3=1.259712.$

   Step 4 — Compute

   $A=80000\times1.259712=₹1,00,776.96.$ …

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4. CA Foundation 2026Set jan-20261 markMCQ
   Q.The value of compound interest (in nearest $₹$) if $₹30,00,000$ is deposited in a bank for 1 year at the rate of 16% per annum compounded quarterly is: (A) 5,07,575 (B) 5,78,360 (C) 5,09,576 (D) 5,72,540

   ›Reveal solutionSolution

   $A=30{,}00{,}000\times(1.04)^4=₹35{,}09{,}575.68$, so $CI=A-P\approx₹5{,}09{,}576$.

   Step 1 — Set per-period rate and periods

   Nominal 16% compounded quarterly: rate per quarter $i=16\%/4=4\%=0.04$; number of quarters in 1 year $n=4$.

   Step 2 — Amount

   $A=P(1+i)^n=30{,}00{,}000\times(1.04)^4.$

   $(1.04)^4=1.16985856,$

   so

   $A=30{,}00{,}000\times1.16985856=₹35{,}09{,}575.68.$

   Step 3 — Compound interest

   $CI=A-P=35{,}09{,}575.68-30{,}00{,}000=₹5{,}09{,}575.68\approx₹5{,}09{,}576.$ …

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5. CA Foundation 2026Set jan-20261 markMCQ
   Q.A sum of money lent at compound interest for 2 years at 20% pa would fetch $₹\ 482/\text{-}$ more if the interest was payable half yearly then if it was payable annually. What is the value of sum deposited? (A) ₹ 10,000 (B) ₹ 15,000 (C) ₹ 17,500 (D) ₹ 20,000

   ›Reveal solutionSolution

   Half-yearly CI $=0.4641P$, annual CI $=0.44P$; difference $0.0241P=482\Rightarrow P=₹20,000$.

   Step 1 — Annual compounding

   Rate 20% p.a., 2 years:

   $A=P(1.20)^2=1.44P,\qquad CI_{annual}=0.44P.$

   Step 2 — Half-yearly compounding

   Rate per half-year $=10\%$, periods $=4$:

   $A=P(1.10)^4=1.4641P,\qquad CI_{half}=0.4641P.$

   Step 3 — Set up the difference

   $CI_{half}-CI_{annual}=(0.4641-0.44)P=0.0241P=482.$

   Step 4 — Solve

   $P=\frac{482}{0.0241}=₹20,000.$ …

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6. CA Foundation 2026Set may-20261 markMCQ
   Q.If the difference between the annually compounded interest and simple interest on a certain sum of money at 8% per annum for 3 years is ₹ 788. Then the principle amount is ______. (A) ₹ 39,175 (B) ₹ 39,475 (C) ₹ 39,975 (D) ₹ 40,475

   ›Reveal solutionSolution

   Use the 3-year difference formula $CI-SI=P[(1+r)^3-1-3r]$; solving $788=P(0.019712)$ gives $P\approx ₹39{,}975$.

   Step 1 — Write the difference formula

   For $3$ years the difference between compound interest and simple interest is:

   $CI-SI=P\big[(1+r)^3-1-3r\big]$

   where $r$ is the rate per rupee.

   Step 2 — Substitute $r=0.08$

   $(1.08)^3=1.259712$

   $(1+r)^3-1-3r=1.259712-1-0.24=0.019712$

   Step 3 — Solve for the principal

   $788=P\times 0.019712$

   $P=\frac{788}{0.019712}\approx ₹39{,}975$ …

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7. CA Foundation 2026Set may-20261 markMCQ
   Q.Raju deposit ₹ 20,000 in a nationalized bank for 3 years at an annual interest rate of 8%, with the interest compounded every quarter. Find out how much interest Raju earns in the first year and the second year. (A) ₹ 1,632 & ₹ 1,712 (B) ₹ 1,684 & ₹ 1,738 (C) ₹ 1,648 & ₹ 1,784 (D) ₹ 1,696 & ₹ 1,746

   ›Reveal solutionSolution

   With 2% per quarter the annual growth factor is $(1.02)^4-1\approx0.08243$; applying it year by year gives interest of ₹1,648 (year 1) and ₹1,784 (year 2).

   Step 1 — Find the quarterly rate and annual factor

   Nominal $8\%$ p.a. compounded quarterly $\Rightarrow$ $2\%$ per quarter. In one year (4 quarters) the balance grows by:

   $(1.02)^4=1.082432\ \Rightarrow\ \text{annual interest factor}=0.082432$

   Step 2 — First year's interest

   $I_1=20{,}000\times 0.082432\approx ₹1{,}648.6\approx ₹1{,}648$

   Balance at end of year 1 $=20{,}000+1{,}648.6=₹21{,}648.6$.

   Step 3 — Second year's interest

   The same factor now acts on the larger balance:

   $I_2=21{,}648.6\times 0.082432\approx ₹1{,}784.5\approx ₹1{,}784$ …

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8. CA Foundation 2026Set may-20261 markMCQ
   Q.The compound interest for ₹ 15,000 at 20% per annum for 2 years compounded semi-annually is ________. (A) ₹ 9,661.50 (B) ₹ 6,961.50 (C) ₹ 9,691.50 (D) ₹ 6,696.15

   ›Reveal solutionSolution

   Half-year rate $10\%$, $4$ periods: $A=15000(1.1)^4=21961.50$, CI $=A-P=6961.50$.

   Step 1 — Adjust rate and periods for semi-annual compounding

   Rate per period $=\dfrac{20\%}{2}=10\%$; number of periods $=2\times 2=4$.

   Step 2 — Compound amount

   $A = P\left(1+\frac{i}{2}\right)^{2n} = 15000(1.10)^4$

   $= 15000 \times 1.4641 = ₹21{,}961.50$

   Step 3 — Compound interest

   $\text{CI} = A - P = 21961.50 - 15000 = ₹6{,}961.50$

   Why the other options are wrong

   • (A) ₹9,661.50 and (C) ₹9,691.50 mistakenly report an amount-like figure or use a wrong power.
   • (D) ₹6,696.15 is a digit-transposed distractor of the correct 6,961.50. …

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9. CA Foundation 2026Set may-20261 markMCQ
   Q.In how many years will ₹ 50,000 become ₹ 75,000 at 8% per annum compound interest? (Given log(1.5)= 0.1761 and log(1.08) = 0.0334) (A) 4.8 years (B) 5.1 years (C) 5.3 years (D) 5.6 years

   ›Reveal solutionSolution

   Set $(1.08)^n = \tfrac{75000}{50000} = 1.5$ and take logarithms: $n = \dfrac{\log 1.5}{\log 1.08} = \dfrac{0.1761}{0.0334} \approx 5.3$ years.

   Step 1 — Compound-interest growth equation

   $A = P(1+i)^{n}$

   Step 2 — Form the ratio

   $P=50000$, $A=75000$, $i=8\%=0.08$:

   $(1.08)^{n} = \frac{75000}{50000} = 1.5$

   Step 3 — Take logarithms and solve

   $n\,\log(1.08) = \log(1.5) \;\Rightarrow\; n = \frac{\log 1.5}{\log 1.08} = \frac{0.1761}{0.0334}$

   $n = 5.27 \approx 5.3\ \text{years}$

   Why the other options are wrong: (A) 4.8, (B) 5.1 and (D) 5.6 do not equal $0.1761/0.0334$; they come from mis-dividing or rounding early. …

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10. CA Foundation 2025Set jan-20251 markMCQ
    Q.Anil deposited a certain amount in a bank at the rate of 10% per annum compounded semi-annually. At the end of one year Anil received a sum of ₹ 13,230. Then the sum deposited in the bank is (A) ₹ 13,000 (B) ₹ 1,200 (C) ₹ 12,000 (D) ₹ 5,000

    ›Reveal solutionSolution

    Semi-annual: $i = 5\%$, $n = 2$; $P(1.05)^2 = 13230 \Rightarrow P = ₹12,000$.

    Step 1 — Adjust rate and periods for semi-annual compounding

    Nominal 10% p.a. compounded semi-annually → rate per half-year $= 5\%$, number of half-years in 1 year $= 2$.

    Step 2 — Apply the compound amount formula

    $A = P(1 + i)^n = P(1.05)^2 = 1.1025\,P$

    Step 3 — Solve for the deposit

    $1.1025\,P = 13230 \Rightarrow P = \frac{13230}{1.1025} = 12000$

    Why the other options are wrong: (A) ₹13,000 is close to the maturity value, not the deposit; (B) ₹1,200 and (D) ₹5,000 are off by an order of magnitude / do not compound to ₹13,230. …

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11. CA Foundation 2025Set jan-20251 markMCQ
    Q.What is the present value of ₹ 8,000 to be required after 10 years if the interest rate be 6% ? (Given that $(1.06)^{10} = 1.7908$) (A) ₹ 6,499.87 (B) ₹ 4,467.28 (C) ₹ 5,867.32 (D) ₹ 1,790.86

    ›Reveal solutionSolution

    $PV = \dfrac{8000}{(1.06)^{10}} = \dfrac{8000}{1.7908} = ₹4,467.28$.

    Step 1 — Identify a single-sum present value

    A single amount $FV = ₹8,000$ is due after $n = 10$ years; discount it at $i = 6\% = 0.06$.

    Step 2 — Apply the discounting formula

    $PV = \frac{FV}{(1+i)^n} = \frac{8000}{(1.06)^{10}}$

    Step 3 — Substitute and compute

    $PV = \frac{8000}{1.7908} = 4467.28$

    Why the other options are wrong: (A) ₹6,499.87 and (C) ₹5,867.32 under-discount the amount; (D) ₹1,790.86 is essentially the discount FACTOR $\times 1000$, not the present value. …

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12. CA Foundation 2025Set jan-20251 markMCQ
    Q.A certain amount is invested in a bank. What annual rate of interest compounded annually becomes 8 times of this investment in 5 years ? (Given that $8^{1/5} = 1.515716$) (A) 51.57% (B) 5.15% (C) 15.15% (D) 1.51%

    ›Reveal solutionSolution

    If money becomes 8 times in 5 years, then $(1+r)^5 = 8 \Rightarrow r = 8^{1/5} - 1 = 51.57\%$.

    Step 1 — Set up the compound-interest equation

    Under annual compounding the amount after $n$ years is $A = P(1+r)^n$. Here the amount becomes 8 times the principal in 5 years, so $A = 8P$ and $n = 5$.

    $8P = P(1+r)^5 \;\Rightarrow\; (1+r)^5 = 8$

    Step 2 — Take the 5th root

    $1 + r = 8^{1/5} = 1.515716$

    $r = 1.515716 - 1 = 0.515716$

    Step 3 — Convert to a percentage

    $r = 0.515716 \times 100 \approx 51.57\%$

    Why the other options are wrong: (B) 5.15% and (D) 1.51% are decimal-shift errors on the correct digits; (C) 15.15% wrongly reads $8^{1/5}$ as giving 0.1515. …

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