Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7937.5
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
$7937.5 = P (1 + 5% × 5)
⇒ $7937.5 = P (1 + 5/100 × 5)
⇒ $7937.5 = P (1 + 5 × 5/100)
⇒ $7937.5 = P (1 + 25/100)
⇒ $7937.5 = P (100 + 25/100)
⇒ $7937.5 = P × 125/100
⇒ P × 125/100 = $7937.5
⇒ P = 7937.5/125/100
⇒ P = 7937.5 × 100/125
⇒ P = 7937.5 × 100/125
⇒ P = 793750/125
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7937.5, then the Principal = 100/125 × 7937.5
= 100 × 7937.5/125
= 793750/125
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(8) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.