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) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(2) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(4) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(6) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.