Question:
How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6325
Rate of Simple Interest (R) = 3%
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
$6325 = P (1 + 3% × 5)
⇒ $6325 = P (1 + 3/100 × 5)
⇒ $6325 = P (1 + 3 × 5/100)
⇒ $6325 = P (1 + 15/100)
⇒ $6325 = P (100 + 15/100)
⇒ $6325 = P × 115/100
⇒ P × 115/100 = $6325
⇒ P = 6325/115/100
⇒ P = 6325 × 100/115
⇒ P = 6325 × 100/115
⇒ P = 632500/115
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 = 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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6325, then the Principal = 100/115 × 6325
= 100 × 6325/115
= 632500/115
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(3) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(7) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(10) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.