Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6540
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
$6540 = P (1 + 4% × 5)
⇒ $6540 = P (1 + 4/100 × 5)
⇒ $6540 = P (1 + 4 × 5/100)
⇒ $6540 = P (1 + 20/100)
⇒ $6540 = P (100 + 20/100)
⇒ $6540 = P × 120/100
⇒ P × 120/100 = $6540
⇒ P = 6540/120/100
⇒ P = 6540 × 100/120
⇒ P = 6540 × 100/120
⇒ P = 654000/120
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 6540, then the Principal = 100/120 × 6540
= 100 × 6540/120
= 654000/120
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(2) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(8) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?