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Maths-

General

Easy

Question

The Simple interest on a sum of money for 2 years at 4% per annum is Rs340. Find (i) the sum of Money and (ii) the compound interest on this sum for one year payable half-yearly at the same rate

hint Hint:

Use the formula of simple interest to get the principal amount and from that find the compound interest.

The correct answer is: 171.4 Rs

Complete step by step solution:
(i) We calculate simple interest by the formula, $S I equals fraction numerator P T R over denominator 100 end fraction$ …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here we have R = 4% ,T = 2 years ,SI = 340 Rs and P = ?
On substituting the known values in (i), we have $340 equals fraction numerator p cross times 2 cross times 4 over denominator 100 end fraction$
$table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow P equals fraction numerator 340 cross times 100 over denominator 2 cross times 4 end fraction end cell row cell not stretchy rightwards double arrow P equals 34000 over 8 end cell end table$
$not stretchy rightwards double arrow P equals 4250$ Rupees
(ii) We know that compound interest = Total amount - principal amount that is, CI = A - P …(ii)
Here we have $A equals P open parentheses 1 plus R over 100 close parentheses to the power of 2 T end exponent$ …(iii)
Here, we have T = 1 (payable half yearly), P = 4250 , R = $4 over 2$ = 2% and A = ?
On substituting the known values in (iii), we get $A equals 4250 open parentheses 1 plus 2 over 100 close parentheses squared$
On substituting the known values in (ii), we get $C I equals 4250 open parentheses 1 plus 2 over 100 close parentheses squared minus 4250$
$not stretchy rightwards double arrow C I equals 4250 cross times open parentheses 51 over 50 close parentheses squared minus 4250$
$rightwards double arrow$ CI = 171.7 Rs

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