Calculate the amount of Rs 12000 for 2 years at 10 per annum compound interest

Principal for the first year = Rs 12000

Rate of interest = 10% p.a.

Interest for the first year = Rs (12000 × 10 × 1) / 100

= Rs 1200

Amount at the end of first year = Rs 12000 + Rs 1200

= 13200

Principal for the second year = Rs 13200

Interest for the second year = Rs (13200 × 10 × 1) / 100

= Rs 1320

Amount at the end of second year = Rs 13200 + Rs 1320

= Rs 14520

Principal for the third year = Rs 14520

Interest for the third year = Rs (14520 × 10 × 1) / 100

= Rs 1452

Amount at the end of third year = Rs 14520 + Rs 1452

= Rs 15972

Hence,

Compound interest for 3 year = Final amount – (original) Principal

= Rs 15972 – Rs 12000

= Rs 3972

Answer

Verified

Hint: Use compound interest formula which is given as $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}-P$, where ‘r’ is interest in percentage, ‘n’ is time period in years, ‘P’ is principal amount and ‘A’ is amount after ‘n’ years.

Complete step-by-step answer:
We know that the amount ‘A’ at the end of ‘n’ years at the rate of r% per annum when the interest is compounded annually is given by,
$A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}...........\left( i \right)$
Where P = Initial amount or principal amount that increases by r % annually.
Here, we have 12000 as the principal amount which is increasing at a rate of 12% for the time period of 10 years.
Hence, from the given equation, we have
P = 12000 Rs
r = 12%
n = 10 years
Now, using the equation, we can get amount ‘A’ after 10 years as,
$\begin{align}
  & A=12000{{\left( 1+\dfrac{12}{100} \right)}^{10}} \\
 & A=12000{{\left( 1+\dfrac{3}{25} \right)}^{10}} \\
\end{align}$
Now, taking LCM inside the bracket, we get
$A=12000{{\left( \dfrac{28}{25} \right)}^{10}}...........\left( ii \right)$
Now, we can solve equation (ii) by multiplying $\dfrac{28}{25}$ to 10 times. But this process would be very lengthy for calculating the value of ‘A’.
So, we can use logarithm and antilogarithm to get value of A as follows
Taking log to both sides to equation (ii), we get.
$\log A=\log \left( \left( 12000 \right){{\left( \dfrac{28}{25} \right)}^{10}} \right)..........\left( iii \right)$
We can use identity of logarithm as
log ab = log a + log b
Applying above identity with equation (iii) we get,
$\log A=\log 12000+\log {{\left( \dfrac{28}{25} \right)}^{10}}$
Now, we can use another identity of ‘log’ as
$\log {{m}^{n}}=n\log m$
So, we get
$\log A=\log 12000+10\log \dfrac{28}{25}........\left( iv \right)$
We have another identity of logarithm
$\log \left( \dfrac{a}{b} \right)=\log a-\log b$
Hence, equation (iv) can be given as
$\log A=\log 12+\log 1000+10\left( \log 28-log25 \right)$
Now, we get values of logarithms of above by using logarithm table as
log 28 = 1.4472
log 25 = 1.3979
log 12 = 1.0792
log 1000 = $\log {{10}^{3}}$ = 3log 10 = 3
Hence, on putting values in above equation, we get
log A = 4.0792 + 0.493
log A = 4.5722
Taking antilog to both sides, we get
A = antilog (4.5722) = 37350
So, the amount after 10 years is Rs 37350.
As we know compound interest can be given by relation.
Compound interest = Total amount after interest – principal value/amount.
So, compound interest after 10 years is,
 37350 – 12000 = Rs.25350

Note: One may apply the formula of simple interest as $\dfrac{P\times R\times T}{100}$ where ‘P’ is principal amount, ‘R’ is interest and ‘T’ is time period but that has become wrong. So, be clear with both terms i.e simple and compound interest. One can answer compound interest as ‘A’ i.e. total amount after 10 years. So, don’t confuse compound interest and total amount.

hi welcome to the sweet you and the question is calculate the amount and the compound interest on rupees 12000 into your eyes at 10% for your sofa waterfall latest write a given conditions in this question so Kiya principal is equal to rupees 12000 time period that is t is equal to 2 years and says the interest is compounded annually to the value of n small and will equal to 2 and rate of interest is 10% per annum now let is supplied the formula of amount so that we can get the value of a mountain of that will calculate the compound interest amount we know that it is equal to P in bracket 1 + aw100 to the power and now put all the given value here so amount will be equal to 12000

in bracket 1 + net is 10% over 100 to the power to simplify this equation Y is equal to 12000 in bracket solving this bracket will get 180 nominator and 110 in the numerator and can cancel this 10 with ac so finally we will get amount is equal to 12000 into 11 by 10 into 11 by then we can cancel these two zeros with these two so amount will come out to be 120 into 11 into 11 and this will give us the value of amount equals to 14005 20 so this is the value of M out and from this value of amount will calculate the compound interest so as we know that compound interest is equal to

what amount - principal support the values of amount in principal amount is 14005 20 - principle is 12000 so from this we will get the value of compound interest equals to 2520 so this is the value of component these are the final answer I hope you have got this thank you

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