Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7302.5
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
$7302.5 = P (1 + 3% × 5)
⇒ $7302.5 = P (1 + 3/100 × 5)
⇒ $7302.5 = P (1 + 3 × 5/100)
⇒ $7302.5 = P (1 + 15/100)
⇒ $7302.5 = P (100 + 15/100)
⇒ $7302.5 = P × 115/100
⇒ P × 115/100 = $7302.5
⇒ P = 7302.5/115/100
⇒ P = 7302.5 × 100/115
⇒ P = 7302.5 × 100/115
⇒ P = 730250/115
⇒ 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 = 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 7302.5, then the Principal = 100/115 × 7302.5
= 100 × 7302.5/115
= 730250/115
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(5) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(9) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.