Question:
If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5376
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$5376 = P (1 + 3% × 4)
⇒ $5376 = P (1 + 3/100 × 4)
⇒ $5376 = P (1 + 3 × 4/100)
⇒ $5376 = P (1 + 12/100)
⇒ $5376 = P (100 + 12/100)
⇒ $5376 = P × 112/100
⇒ P × 112/100 = $5376
⇒ P = 5376/112/100
⇒ P = 5376 × 100/112
⇒ P = 5376 × 100/112
⇒ P = 537600/112
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5376, then the Principal = 100/112 × 5376
= 100 × 5376/112
= 537600/112
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(2) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(5) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(8) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.