Question:
If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4928
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
$4928 = P (1 + 3% × 4)
⇒ $4928 = P (1 + 3/100 × 4)
⇒ $4928 = P (1 + 3 × 4/100)
⇒ $4928 = P (1 + 12/100)
⇒ $4928 = P (100 + 12/100)
⇒ $4928 = P × 112/100
⇒ P × 112/100 = $4928
⇒ P = 4928/112/100
⇒ P = 4928 × 100/112
⇒ P = 4928 × 100/112
⇒ P = 492800/112
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 4928, then the Principal = 100/112 × 4928
= 100 × 4928/112
= 492800/112
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(5) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(8) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.