CA Foundation Exam > CA Foundation Questions > A man lent Rs 1,600 on compound interest pert...
Start Learning for Free
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?
Most Upvoted Answer
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...
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup