A person invested Rs. 46875 at some rate of compound interest for 3 years. At the end of 3 years he receives Rs. 12174 as interest. Find the rate of compound interest.
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- 10%
- 8%
- 12%
- 6%
- 9%
Answer (Detailed Solution Below)
Option 2 : 8%
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Simplification (Start your practice)
10 Questions 10 Marks 10 Mins
GIVEN :
A person invested Rs.46875 at compound interest for 3 years.
The interest received at the end of 3 years is Rs.12174.
FORMULA USED :
C.I. = P(1 + r/100)n - P
Where,
C.I. = Compound Interest
P = Principal
r = rate of interest
n = number of years
CALCULATION :
C.I. = P(1 + r/100)n - P
⇒ 12174 = 46875(1 + r/100)3 - 46875
⇒ 12174 + 46875 = 46875(1 + r/100)3
⇒ 59049 = 46875(1 + r/100)3
⇒ 19683/15625 = (1 + r/100)3
⇒ 27/25 = 1 + r/100
⇒ 27/25 - 1 = r/100
⇒ 2/25 = r/100
⇒ r = 8%
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Surat question of the question in which a man invested rupees 46875 iterate 4% per annum compound interest for that reason calculate the interest for the show at compound interest product first year compound interest is equal to principal oneplus Hue 2200 time sunao window the principal amount 46875 oneplus weight is 4% in time time to calculate interest only for the first year so here we have an equal to food Tech Kotak 87500 plus 4 divided 500 power bond is no need to
write one so we have 46875 into 10 420 writers 46875 into 1.04 now we can do the multiplying of both 46875 into 10 20 year 30 year 35 year 27 year 180 there is no need to X 0 X 15786 equal 200 10 50 equal to 48750 thankyou
Answer
Verified
Hint: Here, in the given question, we have been asked to find the compound interest given the initial principal amount, rate of interest and time period. We will simply use the formula of compound interest. But remember, compound interest formula gives us the final amount i.e. principal amount plus the interest earned for the period. To calculate only the interest, we will subtract the principal amount.
Formula used:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}\],
where
\[A\] = total amount (principal plus interest)
\[P\] = Principal amount
\[R\] = Rate of interest
\[N\] = time (in years)
Complete step-by-step answer:
I.Given: Principal Amount \[\left( P \right)\] = ₨\[46,875\]
Rate of interest \[\left( R \right) = 4\% p.a.\]
To calculate: interest for the first year
We have \[P = 46875\], \[R = 4\% \], \[N = 1\]
Using compound interest formula which is given by \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}\]
\[
A
= 46,875{\left( {1 + \dfrac{4}{{100}}} \right)^1} \\
\Rightarrow A = 46,875\left( {\dfrac{{104}}{{100}}} \right) \\
\Rightarrow A = 48750 \;
\]
We get the total amount after first year as ₨\[48750\].
Interest for first year = Total amount – Principal
\[
= 48750 - 46875 \\
= 1875 \;
\]
II.To calculate: the amount standing to his credit at the end of the second year
We have \[P
= 46875\], \[R = 4\% \], \[N = 2\], Therefore,
\[
A = 46875{\left( {1 + \dfrac{4}{{100}}} \right)^2} \\
A = 46875{\left( {\dfrac{{104}}{{100}}} \right)^2} \\
A = 50700 \;
\]
III.To calculate: the interest for the third year
We have \[P = 46875\], \[R = 4\% \], \[N = 3\], Therefore,
\[
A = 46875{\left( {1 + \dfrac{4}{{100}}} \right)^3} \\
A = 46875{\left( {\dfrac{{104}}{{100}}} \right)^3}
\\
A = 52728 \;
\]
We get the total amount after three year as ₨\[52728\].
Interest for third year = Total amount – Principal
\[
= 52728 - 50700 \\
= 2028 \;
\]
I.₨\[1,875\]
II.₨\[50,700\]
III.₨\[2,028\]
Note: We should understand that the compound interest for the first year is the same as the simple interest for the first year. We could simply use a simple interest formula to calculate the first year of interest which is given as \[S.I. = \dfrac{{PRT}}{{100}}\], where \[P,R,T\] denotes principal amount, rate of interest and time in years respectively.