Question:
Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4200
Rate of Simple Interest (R) = 4%
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
$4200 = P (1 + 4% × 3)
⇒ $4200 = P (1 + 4/100 × 3)
⇒ $4200 = P (1 + 4 × 3/100)
⇒ $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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 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) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(6) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(9) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.