The difference between compound interest and simple interest at the same rate o

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Question

The difference between compound interest and simple interest at the same rate on Rs 5000 for 2 years is Rs 72. The rate of interest per annum is:

Options:

A . 6%

B . 8%

C . 10%

D . 12%

Answer: Option D

Let the rate be r % p.a,
Then
S. I = Rs (5000 — r/100 — 2) = Rs (100r)
C. I = Rs[5000 — (1 + r/100) ² - 5000]
= Rs {5000 — [(1 + r/100) ² “ 1]}
= Rs [5000 — (r²/2 + r/50)]

= Rs (r² /2 + 100r)
(C.I) “ (S.I) = (r²/2 + 100r) “ (100r) = r²/2
Therefore, r²/2 = 72
=> r² = 144
=> r = 12
Hence, Rate = 12 % p.a

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