Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9027.5
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
$9027.5 = P (1 + 3% × 5)
⇒ $9027.5 = P (1 + 3/100 × 5)
⇒ $9027.5 = P (1 + 3 × 5/100)
⇒ $9027.5 = P (1 + 15/100)
⇒ $9027.5 = P (100 + 15/100)
⇒ $9027.5 = P × 115/100
⇒ P × 115/100 = $9027.5
⇒ P = 9027.5/115/100
⇒ P = 9027.5 × 100/115
⇒ P = 9027.5 × 100/115
⇒ P = 902750/115
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 9027.5, then the Principal = 100/115 × 9027.5
= 100 × 9027.5/115
= 902750/115
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(4) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(7) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(9) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?