Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6300
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$6300 = P (1 + 4% × 5)
⇒ $6300 = P (1 + 4/100 × 5)
⇒ $6300 = P (1 + 4 × 5/100)
⇒ $6300 = P (1 + 20/100)
⇒ $6300 = P (100 + 20/100)
⇒ $6300 = P × 120/100
⇒ P × 120/100 = $6300
⇒ P = 6300/120/100
⇒ P = 6300 × 100/120
⇒ P = 6300 × 100/120
⇒ P = 630000/120
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6300, then the Principal = 100/120 × 6300
= 100 × 6300/120
= 630000/120
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(8) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(10) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.