Shortcut:
If Principle = Rs P
Time = t years
Rate = r
and interest is compounded quarterly, then amount is given by
A = P[ 1 +
r/4
/
100
] ^{4t}
Here, t = 5/4, P = 2000, r = 10
Using these values in shortcut, we get:
A = 2000[ 1 +
10/4
/
100
] ^{4 x 5/4}
= 2000[ 1 +
5/2
/
100
] ^{5}
= 2000[ 1 +
1
/
40
] ^{5}
= 2000[
40 + 1
/
40
] ^{5}
= 2000[
41
/
40
] ^{5}
= 2000 x
41 x 41 x 41 x 41 x 41
/
40 x 40 x 40 x 40 x 40
=
41 x 41 x 41 x 41 x 41
/
2 x 4 x 4 x 40 x 40
= 2262.81
∴ the amount is Rs 2262.81.
Now, I = A − P = 2262.81 − 2000 = 262.81
Hence, the compound interest is Rs 262.81
