Example 9 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Example 9 What is the amount we get back if we invest ₹6000 at an interest rate of 10% p.a. for ‘t’ years?Here, we have to consider both examples Simple Interest Compound Interest Now, given that Principal = P = ₹ 6,000 Rate = R = 10% per year = 10/100 = = 1/10 Time = t years Comparing both side-by-side Without Compounding This is simple interest Now, Interest = Principal × Rate × Time = P × R × T = 6,000 × 𝟏/𝟏𝟎 × t = 600t And, Amount = Principal + Interest = 6,000 + 600t With Compounding This is compound interest Thus, Amount = 𝑨 =𝑷(𝟏+𝒓)^𝒕 = 6,000 × (1+1/10)^𝑡 = 6,000 × ((10 + 1)/10)^𝑡 = 𝟔,𝟎𝟎𝟎 × (𝟏𝟏/𝟏𝟎)^𝒕 General Formula For 𝑝= principal, 𝑟= rate as a decimal, 𝑡= time) We can put General Formula as Simple Interest Formula: " Amount "=𝒑(𝟏+𝒓𝒕) Compound Interest Formula: " Amount "=𝒑(𝟏+𝒓)^𝒕