Question

A trader owes a merchant Rs.10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum, how much cash should he pay?
$
  {\text{A}}{\text{. Rs}}{\text{.9025}}{\text{.20}} \\
  {\text{B}}{\text{. Rs}}{\text{.9200}} \\
  {\text{C}}{\text{. Rs}}{\text{.9600}} \\
  {\text{D}}{\text{. Rs}}{\text{.9560}} \\
$

Answer 1

Hint: To find the cash to be paid to settle the account after 3 months, we calculate the P.W. interest using its formula for 9 months. PW stands for ‘present worth’, it gives us the current value of our debt with respect to the time and the amount taken.

Complete step-by-step answer:
We know
${\text{P}}{\text{.W}}{\text{. = }}\dfrac{{100{\text{ }} \times {\text{ Amount}}}}{{100{\text{ + }}\left( {{\text{R}} \times {\text{T}}} \right)}}$
Where Amount is the actual amount, R is the rate of interest percent and T is the time (in years).
The trader wants to settle the account after 3 months, and given the amount is due 1 year
Therefore T = 12 – 3 = 9.
Now,
 $
  {\text{P}}{\text{.W}}{\text{. = }}\dfrac{{100{\text{ }} \times {\text{ 10028}}}}{{100{\text{ + }}\left( {12 \times \dfrac{9}{{12}}} \right)}} \\
   \Rightarrow {\text{P}}{\text{.W}}{\text{. = }}\dfrac{{{\text{1002800}}}}{{100{\text{ + }}\left( 9 \right)}} \\
   \Rightarrow {\text{P}}{\text{.W}}{\text{. = Rs}}{\text{.9200}} \\
$
Hence the amount of cash trader should pay is Rs.9200.
Hence Option B is the correct answer.

Note: In order to solve this type of questions the key is to identify the time reduced to 9 months as the trader wishes to pay after 3 months. Having adequate knowledge in concepts of TW interest is required. Interest is calculated on present worth.