Answer :
Let the sum be P.
Let the interest be compounded annually.
Accumulated total = S1 = P (1 + 20/100)² = P 1.2² = 1.44 P
Interest I1 = accumulated sum - Principal = S1 - P
= 1.44 P - P = (1.44 - 1) P = 0.44 P
If the interest is compounded half-yearly, then:
interest for 6 months = 20% * 6/12 = 10%
number of times it is compounded is 4.
S2 = P ( 1 + 10/100)⁴ = P 1,1⁴ = 1.4641 P
Interest I2 = accumulated sum - Principal = S2 - P
= 1.4641 P - P = (1.4641 - 1) P = 0.4641 P
Difference in the interest = S2 - S1 = I2 - I1 = 0.4641 P - 0.44 P
0.0241 P = Rs 482
P = Sum lent = Rs 20,000.
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Shorter method: It is not necessary to compute Interests separately. Difference in the accumulated sums also gives difference between interests.
Accumulated sum in case of compounding every 1 year
= P (1 + 20/100)² = P 1.2² = 1.44 P
Accumulated sum in case of compounding every 6 months
= P (1 + 10/100)⁴ = P 1.1⁴ = 1.4641 P
So difference = 0.0241 P = Rs 482
P = Rs 20,000
Let the interest be compounded annually.
Accumulated total = S1 = P (1 + 20/100)² = P 1.2² = 1.44 P
Interest I1 = accumulated sum - Principal = S1 - P
= 1.44 P - P = (1.44 - 1) P = 0.44 P
If the interest is compounded half-yearly, then:
interest for 6 months = 20% * 6/12 = 10%
number of times it is compounded is 4.
S2 = P ( 1 + 10/100)⁴ = P 1,1⁴ = 1.4641 P
Interest I2 = accumulated sum - Principal = S2 - P
= 1.4641 P - P = (1.4641 - 1) P = 0.4641 P
Difference in the interest = S2 - S1 = I2 - I1 = 0.4641 P - 0.44 P
0.0241 P = Rs 482
P = Sum lent = Rs 20,000.
==================================
Shorter method: It is not necessary to compute Interests separately. Difference in the accumulated sums also gives difference between interests.
Accumulated sum in case of compounding every 1 year
= P (1 + 20/100)² = P 1.2² = 1.44 P
Accumulated sum in case of compounding every 6 months
= P (1 + 10/100)⁴ = P 1.1⁴ = 1.4641 P
So difference = 0.0241 P = Rs 482
P = Rs 20,000