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) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(4) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.