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A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum?
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A man lent Rs 1,600 on compound interest pertly at 8% per annum compou...
Given:
Principal amount = Rs 1,600
Interest rate at 8% per annum compounded annually
Interest rate at 9% per annum compounded semi-annually
Total interest received after one year = Rs 142.43
To Find:
Amount lent at 8% per annum
Let the amount lent at 8% per annum be x
Then, the amount lent at 9% per annum will be (1600 - x)
Using the formula for compound interest, we get:
Amount = P(1 + R/100)^n
where P is the principal amount, R is the rate of interest, and n is the number of years
Amount obtained at 8% per annum after one year = x(1 + 8/100)^1 = x(1.08)
Interest obtained at 9% per annum compounded semi-annually after one year can be calculated as follows:
Amount after 1st half-year = (1600 - x)(1 + 9/100/2)^1 = (1600 - x)(1.045)
Amount after 2nd half-year = (1600 - x)(1 + 9/100/2)^2 = (1600 - x)(1.045)^2
Total amount obtained at the end of the year = (1600 - x)(1.045)^2 + x(1.08)
Total interest received after one year = Total amount obtained - Principal amount
142.43 = (1600 - x)(1.045)^2 + x(1.08) - 1600
142.43 = (1600 - x)(1.092025) + x(1.08) - 1600
142.43 = 1748.84 - 1.092025x + 1.08x - 1600
142.43 = 148.84 + 0.012025x
0.012025x = 142.43 - 148.84
0.012025x = -6.41
x = -6.41/0.012025
x = 533.22
Therefore, the amount lent at 8% per annum is Rs 533.22.
Principal amount = Rs 1,600
Interest rate at 8% per annum compounded annually
Interest rate at 9% per annum compounded semi-annually
Total interest received after one year = Rs 142.43
To Find:
Amount lent at 8% per annum
Step-by-Step Solution:
Let the amount lent at 8% per annum be x
Then, the amount lent at 9% per annum will be (1600 - x)
Interest obtained at 8% per annum:
Using the formula for compound interest, we get:
Amount = P(1 + R/100)^n
where P is the principal amount, R is the rate of interest, and n is the number of years
Amount obtained at 8% per annum after one year = x(1 + 8/100)^1 = x(1.08)
Interest obtained at 9% per annum:
Interest obtained at 9% per annum compounded semi-annually after one year can be calculated as follows:
Amount after 1st half-year = (1600 - x)(1 + 9/100/2)^1 = (1600 - x)(1.045)
Amount after 2nd half-year = (1600 - x)(1 + 9/100/2)^2 = (1600 - x)(1.045)^2
Total amount obtained at the end of the year = (1600 - x)(1.045)^2 + x(1.08)
Calculation of Total Interest:
Total interest received after one year = Total amount obtained - Principal amount
142.43 = (1600 - x)(1.045)^2 + x(1.08) - 1600
142.43 = (1600 - x)(1.092025) + x(1.08) - 1600
142.43 = 1748.84 - 1.092025x + 1.08x - 1600
142.43 = 148.84 + 0.012025x
0.012025x = 142.43 - 148.84
0.012025x = -6.41
x = -6.41/0.012025
x = 533.22
Therefore, the amount lent at 8% per annum is Rs 533.22.
Community Answer
A man lent Rs 1,600 on compound interest pertly at 8% per annum compou...
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A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum?
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A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum?.
A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man lent Rs 1,600 on compound interest pertly at 8% per annum compounded annually and partly at 9% per annum compounded semi-annually. If the total interest received after one year was Rs 142.43, how much did he lend at 8% per annum?.
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