Question

Anjali borrowed Rs. 19000 at $6\dfrac{1}{2}\% $ for 2 years. At the end of 2 years, she pays Rs. 15000 and a gold ring to the moneylender. What is the value of the gold ring?

Answer 1

Hint: In mathematics, simple interest is used to calculate the interest on a certain amount. Simple interest is paid at the end of a specific time period and is always a fixed amount that the borrower has to pay. It is calculated by using the formula:
$S.I. = \dfrac{{P \times T \times R}}{{100}}$
After calculating the value of S.I., the principal is added to it to get the total amount that the borrower has to give. Its formula is given by:
${\text{Amount = P + S}}{\text{.I}}{\text{.}}$
In this question, we have to calculate the value of interest then calculate the amount. Here amount is equal to the sum of the amount paid at the end of 2 years and the value of the gold ring.

Complete step by step solution: According to the question,
 Principal (P) = Rs.19000
Rate (R) = $6\dfrac{1}{2}\% = \dfrac{{13}}{2}\% $
Time (T) = 2 years
At the end of 2 years, she will pay back money with interest hence, we have to calculate the simple interest first
Simple Interest (I) = $\dfrac{{P \times T \times R}}{{100}}$
$
  I = \dfrac{{19000 \times 2 \times \dfrac{{13}}{2}}}{{100}} \\
  I = \dfrac{{19000 \times 13}}{{100}} \\
  I = 2470 \\
 $
Therefore, the interest paid on the principal amount is Rs.2470
Amount to be paid at the end of 2 years = \[P + I\;\;\]
$
  {\text{Amount}} = 19000 + 2470 \\
  {\text{Amount}} = Rs.21470 \\
$
Anjali pays Rs.15000 and a gold ring as the amount at the end of 2 years.
So, Amount = 15000 + Value of gold ring
Let the value of gold ring be x,
$
  21470 = 15000 + x \\
  x = 21470 - 15000 \\
  x = 6470 \\
$
Therefore, the value of the gold ring is Rs.6470.

Note: When you borrow money, there is an extra amount to be paid along with the amount you borrowed. That extra money that you pay is known as interest. Simple interest is paid only on the principal amount.