# The difference between compound interest and simple interest on an amount at 10% per annum for 3 years is Rs. 310. If same principal is lends on simpl

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The difference between compound interest and simple interest on an amount at 10% per annum for 3 years is Rs. 310. If same principal is lends on simple interest for 5 years at 20% per annum then find simple interest. (compound interest calculated annually).
1. Rs. 8000
2. Rs. 15000
3. Rs. 12000
4. Rs. 10000

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Correct Answer - Option 4 : Rs. 10000

Let the principal be P.

Rate = R = 10% per annum, Time = n = 3 years

Simple Interest = (P × N × R)/100

When interest is compounded annually:

Amount = P[1 + (R/100)]n

Given,

⇒ CI – SI = 310

Then,

⇒ SI = (P × 10 × 3)/100

⇒ SI = 0.3P

⇒ CI = P[1 + (10/100)]3 – P

⇒ CI = P(1.1)3 – P

⇒ CI = 0.331P

⇒ 310 = 0.331P – 0.3P

⇒ P = Rs. 10000

⇒ SI for 5 years at 20% per annum = (10000 × 5 × 20)/100

⇒ SI = 10000

Simple Interest is Rs. 10000.