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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.
(9) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.