On what sum of money does the difference between the simple interest and compound interest in 2 years at 5% per annum is Rs 15??
Answers
Method - 1:
Given, Time n = 2 years, R = 5%.
(i)
We know that C.I = P[(1 + r/100)^n - 1]
= P[(1 + 5/100)^2 - 1]
= P[(21/20)^2 - 1]
= P[441 - 400/400]
= P[41/400]
(ii)
We know that SI = PTR/100
= P * 2 * 5/100
= 10P/100
= P/10.
Given that Difference between SI and CI 15.
⇒ P(41/400) - (P/10) = 15
⇒ 41P/400 - P/10 = 15
⇒ 41P - 40P = 6000
⇒ P = 6000.
Therefore, the sum = 6000.
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Method - 2:
Given, Time n = 2 years, R = 5%.
Let Sum = 100.
We know that SI = PRT/100
= 100 * 2 * 5/100
= 10.
We know that A = P(1 + r/100)^n
= 100(1 + 5/100)^2
= 100(21/20)^2
= 100(441/400)
= 110.25.
We know that CI = A - P
= 110.25 - 100
= 10.25.
Difference between them is:
⇒ 10.25 - 10
⇒ 0.25.
Given that Difference between them is 15.
⇒ 15/0.25
⇒ 60.
Then, sum = 100 * 60
= 6000.
Therefore, the Sum = 6000.
Hope it helps!