Question:
How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $6250
Rate of Simple Interest (R) = 5%
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
$6250 = P (1 + 5% × 5)
⇒ $6250 = P (1 + 5/100 × 5)
⇒ $6250 = P (1 + 5 × 5/100)
⇒ $6250 = P (1 + 25/100)
⇒ $6250 = P (100 + 25/100)
⇒ $6250 = P × 125/100
⇒ P × 125/100 = $6250
⇒ P = 6250/125/100
⇒ P = 6250 × 100/125
⇒ P = 6250 × 100/125
⇒ P = 625000/125
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 6250, then the Principal = 100/125 × 6250
= 100 × 6250/125
= 625000/125
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(2) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(5) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?