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Maths-

General

Easy

Question

In what period will Rs 12,000 yields Rs3,972 as compound interest at 10% per annum; if compounded every year.

hint Hint:

Use the formula of compound interest to get the number of years.

The correct answer is: 3 Years

Complete step by step solution:
We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
We know that $A equals P open parentheses 1 plus R over 100 close parentheses to the power of T$ …(ii)
Here, we have T = ? years, P = 12000 and R = 10%
On substituting the known values in (ii), we get $A equals 12000 open parentheses 1 plus 10 over 100 close parentheses to the power of T$
Given that CI = 3972,
On substituting the known values in (i), we get $3972 equals 12000 open parentheses 1 plus 10 over 100 close parentheses to the power of T to the power of blank end exponent minus 12000$
On adding 12000 on both the sides, we have $15972 equals 12000 open parentheses 1 plus R over 100 close parentheses to the power of T$
Divide on both sides by 12000.
On dividing we have, $15972 over 12000 equals 12000 over 12000 open parentheses 1 plus R over 100 close parentheses to the power of T$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 1331 over 1000 equals open parentheses 1 plus R over 100 close parentheses to the power of T end cell row cell not stretchy rightwards double arrow open parentheses 11 over 10 close parentheses cubed equals open parentheses 1 plus R over 100 close parentheses to the power of T end cell end table$
$rightwards double arrow$ T = 3 years.
In 3 years, Rs 12000 yields 3972 as compound interest at 10% per annum if compounded every Year.

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