Question:
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?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7620
Rate of Simple Interest (R) = 4%
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
$7620 = P (1 + 4% × 5)
⇒ $7620 = P (1 + 4/100 × 5)
⇒ $7620 = P (1 + 4 × 5/100)
⇒ $7620 = P (1 + 20/100)
⇒ $7620 = P (100 + 20/100)
⇒ $7620 = P × 120/100
⇒ P × 120/100 = $7620
⇒ P = 7620/120/100
⇒ P = 7620 × 100/120
⇒ P = 7620 × 100/120
⇒ P = 762000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7620, then the Principal = 100/120 × 7620
= 100 × 7620/120
= 762000/120
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(2) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(5) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(10) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.