Sol
2
Example 41
A customer, Lord Venkateswara, took a loan of
$10 million from Mr Kuber. In the second year of the
loan period, the interest that accrued to Mr Kuber was
$0.1 million more than that in the first year.
(Assume CI)
At what rate of interest did Kuber lend to Lord
Venkateswara?
b. When will the principal double itself
(approximately)?
a.
2 Exar
Answers
Given :- A customer, Lord Venkateswara, took a loan of $10 million from Mr Kuber. In the second year of the loan period, the interest that accrued to Mr Kuber was
$0.1 million more than that in the first year.
To Find :-
A) At what rate of interest did Kuber lend to Lord Venkateswara ?
Answer :-
→ Principal = $ 10 million = 10 * 10 lakh = 100 lakh = 1 crore .
→ Rate = Let R% per annum .
so,
→ Interest of first year = (P * R * T)/100 = (10000000 * x)/100 = $ 100000x
then,
→ Amount after 1 year = 10000000 + 100000x = $ 100000(100 + x) = Principal for second year.
so,
→ Interest for second year = (P * R * T)/100 = 100000(100 + x) * x/100 = $ 1000x(100 + x)
A/q,
→ 1000x(100 + x) - 100000x = 0.1 million = 100000
→ 100000x - 100000x + 1000x² = 100000
→ 1000x² = 100000
→ x² = 100
→ x = 10% (Ans.)
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Given : A customer, Lord Venkateswara, took a loan of $10 million from Mr Kuber. In the second year of the loan period, the interest that accrued to Mr Kuber was $0.1 million more than that in the first year.
(Assume CI)
To Find : At what rate of interest did Kuber lend to Lord Venkateswara?
b. When will the principal double itself
Solution:
In the second year of the loan period, the interest that accrued to Mr Kuber was $0.1 million more than that in the first year.
this $0.1 million excess interest is basically interest of the interest earned in 1st year.
let say interest earned in 1st year = x million
Then x * R * 1 / 100 = 0.1
=> xR = 10 Eq1
interest earned in 1st year = 10 * R * 1 / 100 = x
=> x = R/10
substituting value of x in Eq1
=> (R/10) R = 10
=> R² = 100
=> R = 10
A = P ( 1 + R/100)ⁿ
A = 2P
=> 2P = P ( 1 + 10/100)ⁿ
=> 1.1ⁿ = 2
=> n = 7.28
Approx 7.3 years principal double itself
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