The difference between the compound interest on a certain sum for the second and the third years at 5% p.a. is rs 42. Find the sum.
Please solve this step by step
Answers
Answer:
The sum will be 1600.
Usual mistake made:
Here the required compound interest are for only 2nd and only 3rd year.
our regular formula of P(1+R/100)^2 includes the interest of 1st year with 2nd and
P(1+R/100)^3 includes 1st,2nd years along with 3rd.
the difference between these two values is not the exact sum. It merely gives a value obtained in step2 given below.
correct process:
now
step 1. remove the 1st yr interest from P(1+R/100)^2 ,for obtaining CI of only 2nd yr i.e., {[P(1+R/100)^2] -[P(1+R/100)] } and
step 2. remove first 2yrs compound interest from P(1+R/100)^3 to get CI of only 3rd year i.e., {[P(1+R/100)^3] -[P(1+R/100)^2] }
step 3: now find the difference between values obtained in step 1 and 2
simplified version:
on solving through above process, it comes down to single formula
D=P(r+1)r^2,
where, D=difference
r=R/100
P= required sum
R=interest rate.
Solving given problem:
42=P[(5/100)+1](5/100)^2
on solving,
P=1600