Question:
Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4251
Rate of Simple Interest (R) = 3%
Time (T) = 3 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$4251 = P (1 + 3% × 3)
⇒ $4251 = P (1 + 3/100 × 3)
⇒ $4251 = P (1 + 3 × 3/100)
⇒ $4251 = P (1 + 9/100)
⇒ $4251 = P (100 + 9/100)
⇒ $4251 = P × 109/100
⇒ P × 109/100 = $4251
⇒ P = 4251/109/100
⇒ P = 4251 × 100/109
⇒ P = 4251 × 100/109
⇒ P = 425100/109
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4251, then the Principal = 100/109 × 4251
= 100 × 4251/109
= 425100/109
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(6) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.