Shantanu borrowed Rs. 2.5 lakh from a bank to purchase one car. If the rate of interest be 6% per annum compounded annually, what payment he will have to make after 2 years 6 months?
A certain amount of money is lent out at compound interest at the rate of 20% per annum for two years, compounded annually. It would give Rs. 482 more if the amount is compounded half yearly. Find the principle.
Approach I: To solve this question, we can apply the net % effect formula
x + y +
xy
%
100
Compounded annually at rate 20% per annum for 2 years, we get
= 20 + 20 +
20 × 20
= 44%
100
Similarly, compounded half yearly at rate 10%, we get
= 10 + 10 +
10 × 10
= 21%
100
And, 21 + 10 +
21 × 10
= 33.1%
100
And, 33.1 + 10 +
33.1 × 10
= 46.41%
100
Now as per the question,
Difference between compound interest yearly and half yearly = 46.41 – 44 = 2.41%
Given, 2.41% ≡ 482
100% ≡ x
⇒ x =
482 × 100
= 20,000
2.41
Approach II:
When compounded annually, the amount received at the end of the period is
A = P
[
1 +
r
]
^{n}
100
When compounded half yearly, the amount received at the end of the period is
A = P
[
1 +
r/2
]
^{2n}
100
Let the principle be P.
Interest on this amount when compounded annually at the rate of 20% per annum = P [(1.20)^{2} − 1]
Interest on this amount when compounded half yearly = P [(1.10)^{4} − 1]
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