Question:
If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4200
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$4200 = P (1 + 3% × 4)
⇒ $4200 = P (1 + 3/100 × 4)
⇒ $4200 = P (1 + 3 × 4/100)
⇒ $4200 = P (1 + 12/100)
⇒ $4200 = P (100 + 12/100)
⇒ $4200 = P × 112/100
⇒ P × 112/100 = $4200
⇒ P = 4200/112/100
⇒ P = 4200 × 100/112
⇒ P = 4200 × 100/112
⇒ P = 420000/112
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4200, then the Principal = 100/112 × 4200
= 100 × 4200/112
= 420000/112
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(9) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.