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

Answer 1

Correct Answer: 121000

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.

1. 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
2. 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)
3. 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)
4. 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
5. Verify Range:
   The calculated instalment is Rs. 121,000, which is within the given range (121000, 121000).

Thus, each instalment is Rs. 121,000.