Question:
Thomas had to pay $4142 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
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4142
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
$4142 = P (1 + 3% × 3)
⇒ $4142 = P (1 + 3/100 × 3)
⇒ $4142 = P (1 + 3 × 3/100)
⇒ $4142 = P (1 + 9/100)
⇒ $4142 = P (100 + 9/100)
⇒ $4142 = P × 109/100
⇒ P × 109/100 = $4142
⇒ P = 4142/109/100
⇒ P = 4142 × 100/109
⇒ P = 4142 × 100/109
⇒ P = 414200/109
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4142, then the Principal = 100/109 × 4142
= 100 × 4142/109
= 414200/109
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(3) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(6) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(10) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.