Question:
Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5450
Rate of Simple Interest (R) = 3%
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
$5450 = P (1 + 3% × 3)
⇒ $5450 = P (1 + 3/100 × 3)
⇒ $5450 = P (1 + 3 × 3/100)
⇒ $5450 = P (1 + 9/100)
⇒ $5450 = P (100 + 9/100)
⇒ $5450 = P × 109/100
⇒ P × 109/100 = $5450
⇒ P = 5450/109/100
⇒ P = 5450 × 100/109
⇒ P = 5450 × 100/109
⇒ P = 545000/109
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5450, then the Principal = 100/109 × 5450
= 100 × 5450/109
= 545000/109
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.