Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $7312.5
Rate of Simple Interest (R) = 5%
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
$7312.5 = P (1 + 5% × 5)
⇒ $7312.5 = P (1 + 5/100 × 5)
⇒ $7312.5 = P (1 + 5 × 5/100)
⇒ $7312.5 = P (1 + 25/100)
⇒ $7312.5 = P (100 + 25/100)
⇒ $7312.5 = P × 125/100
⇒ P × 125/100 = $7312.5
⇒ P = 7312.5/125/100
⇒ P = 7312.5 × 100/125
⇒ P = 7312.5 × 100/125
⇒ P = 731250/125
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7312.5, then the Principal = 100/125 × 7312.5
= 100 × 7312.5/125
= 731250/125
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(3) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(5) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(6) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(9) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.