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Find the amount and the compound interest on ₹ 10,000 for 1whole 𝟏/𝟐 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Find the amount and the compound interest on ₹ 10,000 for 1whole 𝟏/𝟐 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually? 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
8 months ago
Dear Student

P =₹10,000
Rate = 10% per annum = 5% per half year
n =1 whole 1/2years
There will be 3 half years in 1 whole 1/2years
Amount, A =P (1 +R/100 )^n
=₹ [10000(1+5/100 )^3]
=₹ [10000(105/100 )^3]
=₹ 11576.25
C.I. = A − P
=₹ 11576.25 − ₹10000
=₹1,576.25
The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.
The amount for the first year has to be calculated first.
Amount, A =P (1 +R/100 )^n
= ₹ [10000(1+10/100)^1]
= ₹ [10000 × (11/10)^1]
=₹ 11000
By taking₹11,000 as the principal, the S.I. for the next1/2year will be calculated.
S.I. = P x R x T
100
=11000×10×1/2
100
=₹550
∴Interest for the first year =₹ 11000 − ₹10000 =₹1,000
∴Total compound interest =₹1000 +₹550 =₹1,550
∴ The interest would be more when compounded half yearly than the interest when compounded annually.

​Thanks

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