Find the amount and the compound interest on ₹ 10,000 for 3/2 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Here, Principal (P) = ₹ 10000,
Rate of Interest (R) = 10% = 5% (compounded half yearly)
Time (n) = 3/2 years = 3 half-years (compounded half yearly)
Amount (A) = P(1+R/100)ⁿ = 10000(1+ 5/100)³ = 10000(1+1/20)³
= 10000(21/20)³ = 10000 x 21/20 x 21/20 x 21/20 = ₹ 11,576.25
Compound Interest (C.I.) = A – P = ₹ 11,576.25 – ₹ 10,000 = ₹ 1,576.25
If it is compounded annually, then
Here, Principal (P) = ₹ 10000, Rate of Interest (R) = 10%, Time (n) = 3/5 years
Amount (A) for 1 year = P (1+R/100)ⁿ = 10000(1+ 10/100)¹ = 10000(1+ 1/10)¹
= 10000(11/10)¹ = 10000x 11/10 = ₹ 11,000
Interest for 1/2 year = 11000x1x10/2×100 =₹ 550
∴ Total amount = ₹ 11,000 + ₹ 550 = ₹ 11,550
Now, C.I. = A – P = ₹ 11,550 – ₹ 10,000 = ₹ 1,550
Yes, interest ₹ 1,576.25 is more than ₹ 1,550.

Class 8 Maths Chapter 8 Exercise 8.3 Solution in Video

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