Calculate the amount and the compound interest on 12000 in 2 years at 10% per

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.

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

For Ist year

Principal (P) = Rs.12,000

Rate (R) = 10%

Time (T) = 1 year

I = Interest =`(12,000xx10xx1)/100`

= 120 × 10

= Rs.1200

Amount = P + I = Rs.12,000 + Rs.1200 = Rs.13,200

For IInd year

P = Rs.13,200, R = 10%, Time (T) = 1 year

∴ Interest =`(13,200xx10xx1)/100` = 132 × 10 

= Rs.1320

∴ Amount in 2 years = Rs. (13,200) + (1320)

= Rs.14520

Compound interest in 2 years = Rs.1200 + Rs.1320 = Rs.2520

[or directly = Rs.14520 − Rs.12000 = Rs.2520]

Simple interest is a fixed rate of interest applied to the principal amount. Simple interest is calculated only on the original principal amount/quantity. Simply put, simple interests are calculated by taking the product of the principal amount and the rate x the time period.

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How does compounding interest work?

Compound interest is the process of adding interest to the principal. It is the result of reinvesting the interest that you have earned. The more you reinvest, the more you earn. It is also the fastest way to grow your money. However, compounding your interest is not always a good idea.

Compound Interest is calculated each period based on the original principal as well as any interest accrued in previous periods.

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