Question:
Paul had to pay $5123 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
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5123
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
$5123 = P (1 + 3% × 3)
⇒ $5123 = P (1 + 3/100 × 3)
⇒ $5123 = P (1 + 3 × 3/100)
⇒ $5123 = P (1 + 9/100)
⇒ $5123 = P (100 + 9/100)
⇒ $5123 = P × 109/100
⇒ P × 109/100 = $5123
⇒ P = 5123/109/100
⇒ P = 5123 × 100/109
⇒ P = 5123 × 100/109
⇒ P = 512300/109
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 5123, then the Principal = 100/109 × 5123
= 100 × 5123/109
= 512300/109
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(7) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(9) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.