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) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(9) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?