Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $7260
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
$7260 = P (1 + 4% × 5)
⇒ $7260 = P (1 + 4/100 × 5)
⇒ $7260 = P (1 + 4 × 5/100)
⇒ $7260 = P (1 + 20/100)
⇒ $7260 = P (100 + 20/100)
⇒ $7260 = P × 120/100
⇒ P × 120/100 = $7260
⇒ P = 7260/120/100
⇒ P = 7260 × 100/120
⇒ P = 7260 × 100/120
⇒ P = 726000/120
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 7260, then the Principal = 100/120 × 7260
= 100 × 7260/120
= 726000/120
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(6) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.