Question:
John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is
John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is
Updated On: Jul 29, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 121000
Solution and Explanation
To solve the problem, we need to calculate the two equal instalments for a loan of Rs. 2,10,000 at 10% annual compound interest, repaid over two years.
- Calculate the amount after the first year:
The formula for compound interest is:
A = P(1 + r)^n
Here, P = 210000, r = 0.10 (10%), and n = 1 year.
A1 = 210000(1 + 0.10)^1 = 210000 × 1.10 = 231000 - First Instalment:
The first instalment consists of the interest for the first year plus part of the principal.
Interest for the first year = 231000 - 210000 = 21000
Let the first instalment be Rs. X. Then X = 21000 + Y where Y is part of the principal repaid with the first instalment.
Thus, Y = X - 21000; remaining principal = 210000 - Y = 210000 - (X - 21000) - Second Year Calculation:
Remaining principal =(210000 - X + 21000)=231000 - X
A2 = (231000 - X)(1.10)
The second instalment is:
A2 = (231000 - X) × 1.10 = 231000 - X + 0.1*(231000 - X) - Equality of Instalments:
Set the first instalment equal to the second instalment because the condition is that both are equal:
X = (231000 - X) × 1.10
X = 231000 × 1.10 - 1.10X
2.10X = 254100
X = 254100/2.10 = 121000 - Verify Range:
The calculated instalment is Rs. 121,000, which is within the given range (121000, 121000).
Thus, each instalment is Rs. 121,000.
Was this answer helpful?
0
0
Top Questions on SI & CI
- A sum of money triples itself in 8 years at simple interest. In how many years will it become five times itself at the same rate?
- On a certain principal, CI and SI at a certain rate of interest for 2 years is ₹ 16560 and ₹ 14400 respectively. Find the principal and rate of interest per annum.
- ₹ 45000 is deposited at compound interest for 4 years. The rates are 6% (1st year), then increase by 1% each year (so 7%, 8%, 9%). Find the approximate amount at the end of 4 years.
- Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
- S invested 22,000 for 6 years at a 4% rate compounded half-yearly. B also invested a certain amount of money for 5 years in the same scheme and then reinvested it for a year at a 10% rate of simple interest. If their total amounts become the same after 6 years, what was B’s initial investment?
View More Questions
Questions Asked in CAT exam
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
- CAT - 2024
- Time and Work
- Let $a_n$ be the largest integer not exceeding $\sqrt{n}$. Then the value of $a_1 + a_2 + \dots + a_{50}$ is
- CAT - 2024
- Basics of Numbers
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Humans have managed to tweak the underlying biology of various plants and animals to produce high-tech crops and microbes. But regulating these entities is complicated, as the framework of policies and procedures are outdated and not flexible enough to adapt to emerging technology. The question is whether regulation will ever be able to keep up with human innovation, to regulate living things, which are apt to be unpredictable and unique; to capture all the potential risks when new biological entities are introduced, or when they pass on variations of their genes?- CAT - 2024
- Para Summary
View More Questions