Question

the successive interest of 20% three times is equal to a single interest of​

Answer 1

Given :- the successive interest of 20% three times is equal to a single interest of ?

Solution :-

Let Principal is Rs.100x .

so,

→ Amount after 3 years = P[1 + (R/100)]^T

→ A = 100x[1 + (20/100)]³

→ A = 100x[1 + (1/5)]³

→ A = 100x * (6/5)³

→ A = 100x * (216/125)

→ A = 172.8x .

then,

→ Interest recieved = A - P = 172.8x - 100x = Rs.72.8x .

therefore,

→ Rate = (72.8x * 100)/100x = 72.8% (Ans.)

Method 2) :- By formula :-

• successive rate = A + B + AB/100 .
• when A = B , we get = 2A + (A²/100)

so,

→ Successive rate of 20% for 2 years = (2*20) + (20²/100) = 40 + (400/100) = 40 + 4 = 44% .

now,

→ Successive rate of 44% and 20% = 44 + 20 + (44 * 20)/100 = 64 + (88/10) = 64 + 8.8 = 72.8% (Ans.)

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