Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $7480
Rate of Simple Interest (R) = 2%
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
$7480 = P (1 + 2% × 5)
⇒ $7480 = P (1 + 2/100 × 5)
⇒ $7480 = P (1 + 2 × 5/100)
⇒ $7480 = P (1 + 10/100)
⇒ $7480 = P (100 + 10/100)
⇒ $7480 = P × 110/100
⇒ P × 110/100 = $7480
⇒ P = 7480/110/100
⇒ P = 7480 × 100/110
⇒ P = 7480 × 100/110
⇒ P = 748000/110
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7480, then the Principal = 100/110 × 7480
= 100 × 7480/110
= 748000/110
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(8) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(10) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.