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# In what period of time will Rs. 12000 yield Rs. 3,972 as compound interest at 10 percent, if compounded on a yearly basis.  HINT- This is a question based simply on the compound interest. We will use the simple formula of Compound Interest relating with principle, time and rate. The formula used for this question will be $C.I. = P[{(1 + \dfrac{R}{{100}})^n} - 1]$

Now, according to the question-
We have, principal = Rs. 12000
Rate of interest (r) = 10%
Compound interest (C.I.) = Rs. 3972
Time period (n) = ?
From the given formula $C.I. = P[{(1 + \dfrac{R}{{100}})^n} - 1]$
$\Rightarrow 3972 = 12000[{(1 + \dfrac{{10}}{{100}})^n} - 1]$
$\Rightarrow 3972 = 12000[{(\dfrac{{11}}{{10}})^n} - 1]$
$\Rightarrow \dfrac{{3972}}{{12000}} + 1 = {(\dfrac{{11}}{{10}})^n}$
$\Rightarrow \dfrac{{1331}}{{1000}} = {(\dfrac{{11}}{{10}})^n}$
$\Rightarrow {(\dfrac{{11}}{{10}})^3} = {(\dfrac{{11}}{{10}})^n}$
$\Rightarrow n = 3years$
Thus, the time period (n) = 3 years

NOTE- Compound Interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. Interest can be compounded on any given frequency schedule, from continuous to daily to annually. Always remember, when calculating compound interest, the number of compounding periods makes a significant difference. There is also one more concept of Simple Interest, which is calculated on the principal, or original, amount of a loan. The formula for calculating the simple interest is given by-
$S.I. = \dfrac{{P \times R \times T}}{{100}}$ , where P, R, T have their usual meaning as principal, rate, time. Generally, we use compound interest in place of simple interest because it is easy to find it.

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