Question

What annual payment will discharge a debt of Rs.1092 due in 2 year at 12% simple interest?
(a) Rs.725
(b) Rs.325
(c) Rs.515
(d) Rs.900

Answer 1

Hint: In this question the amount Rs.1092 is the money which was taken as a loan on installments for 2 years so first we will find its first installment which will be paid after 1st year and then for second year.
In this question first we will assume an amount which will be paid to the bank which will also be the installment for the second year then we will find the first installments and their sum will be equal to the principle amount so we will find the annual payment.

Complete step by step answer:
Given
Time \[n = 2yrs\]
Rate of simple interest \[r = 12\% \]
Debt amount \[A = Rs.1092\]
Now let installments per year be \[x\]
Now we know the overall amount which we will pay to the bank will be
Interest on Rs. “x” for 1 year + Interest on Rs. “x” for 0 year =1092
Hence we can write this as
\[\left( {x + \dfrac{{12x}}{{100}}} \right) + x = 1092 - - (i)\]
By further solving this equation we get
\[
  \left( {x + \dfrac{{12x}}{{100}}} \right) + x = 1092 \\
   \Rightarrow \dfrac{{100x + 12x + 100x}}{{100}} = 1092 \\
   \Rightarrow 212x = 109200 \\
   \Rightarrow x = 515.09 \\
 \]
Therefore each installment will be \[x = 515.09\]
Hence the annual that will discharge a debt of Rs.1092 due in 2 year at 12% simple interest \[ = Rs.515\]

Option c is correct.

Note: Debt is an amount of money that is borrowed by a person or a company from another person or the company under some given conditions. This amount is borrowed for a time and with a rate of interest by which the borrower will return the money to the lender after the stipulated time.