Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6900
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
$6900 = P (1 + 4% × 5)
⇒ $6900 = P (1 + 4/100 × 5)
⇒ $6900 = P (1 + 4 × 5/100)
⇒ $6900 = P (1 + 20/100)
⇒ $6900 = P (100 + 20/100)
⇒ $6900 = P × 120/100
⇒ P × 120/100 = $6900
⇒ P = 6900/120/100
⇒ P = 6900 × 100/120
⇒ P = 6900 × 100/120
⇒ P = 690000/120
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 6900, then the Principal = 100/120 × 6900
= 100 × 6900/120
= 690000/120
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(6) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(10) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.