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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.