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.
i. Find the rate of compound interest at which he took the loan.
ii. If Aman had taken the same loan at the same rate of interest for 1 year compounded half-yearly, find the amount he would pay at the end of 1 year.
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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Answer:
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 % p.a
Step-by-step explanation: