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Maths-

General

Easy

Question

At what rate % p.a will a sum of Rs4000 yield 1324 as compound interest in 3 yrs

hint Hint:

Use the formula of compound interest to get the rate of interest.

The correct answer is: 10%

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 = 3 years, P = 4000 and R = ?
On substituting the known values in (ii), we get $A equals 4000 open parentheses 1 plus R over 100 close parentheses cubed$
Given that CI = 1324,
On substituting the known values in (i), we get $1324 equals 4000 open parentheses 1 plus R over 100 close parentheses cubed minus 4000$
On adding 4000 on both the sides, we have $5324 equals 4000 open parentheses 1 plus R over 100 close parentheses cubed$
Divide on both sides by 4000.
On dividing we have, $5324 over 4000 equals 4000 over 4000 open parentheses 1 plus R over 100 close parentheses cubed$
$not stretchy rightwards double arrow 1331 over 1000 equals open parentheses 1 plus R over 100 close parentheses cubed$
$not stretchy rightwards double arrow open parentheses 11 over 10 close parentheses cubed equals open parentheses 1 plus R over 100 close parentheses cubed$
$not stretchy rightwards double arrow 11 over 10 equals 1 plus R over 100$
$not stretchy rightwards double arrow R equals 10 straight percent sign$
So, at 10% pa per annum will a sum of Rs 4000 yield 1324 as compound interest in 3 years.

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