Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9375
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
$9375 = P (1 + 5% × 5)
⇒ $9375 = P (1 + 5/100 × 5)
⇒ $9375 = P (1 + 5 × 5/100)
⇒ $9375 = P (1 + 25/100)
⇒ $9375 = P (100 + 25/100)
⇒ $9375 = P × 125/100
⇒ P × 125/100 = $9375
⇒ P = 9375/125/100
⇒ P = 9375 × 100/125
⇒ P = 9375 × 100/125
⇒ P = 937500/125
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = 100/125 × 9375
= 100 × 9375/125
= 937500/125
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(2) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(4) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(7) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.