Aman took a loan of Rs 12,000 from a bank for a period of 2 years compounded
annually. At the end of 2 years, he returned a total of Rs 15,870.
Find the rate of compound Interest at which he took the loan.
Answers
Given : Aman took a loan of Rs 12,000 from a bank for a period of 2 years compounded annually. At the end of 2 years, he returned a total of Rs 15,870.
To Find : the rate of compound Interest
Solution:
P = 12000
R = ?
n = 2 years
A = 15870
A = P (1 + R/100)ⁿ
=> 15870 = 12000 ( 1 + R/100)²
=> 1587 = 1200 ( 1 + R/100)²
=> 529 = 400 ( 1 + R/100)²
=> 23² = 20² ( 1 + R/100)²
=> 23 = 20(1 + R/100)
=> 23/20 = 1 + R/100
=> 23/20 - 1 = R/100
=> 3/20 = R/100
=> R = 15
rate of compound Interest at which he took the loan. = 15 % per annum
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Given :-
- Principal = P = Rs.12000 .
- Time = T = 2 years.
- Amount = A = Rs.15870 .
To Find :-
- Rate of interest per compounded annually ?
Solution :-
we know that, when rate is compounded annually ,
- A = P[1 + (R/100)]^T
- A = Amount .
- P = Principal .
- R = Rate .
- T = Time.
putting all values we get,
→ 15870 = 12000[1 + (R/100)]²
→ 15870/12000 = [1 + (R/100)]²
→ 1587/1200 = [1 + (R/100)]²
→ 529 / 400 = [1 + (R/100)]²
→ (23/20)² = [1 + (R/100)]²
square root both sides ,
→ (23/20) = [1 + (R/100)]
→ (R/100) = (23/20) - 1
→ (R/100) = (23 - 20)/20
→ (R/100) = (3/20)
→ R = (3 * 100) / 20
→ R = 3 * 5
→ R = 15 % per annum (Ans.)
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