Question:
How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $7375
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
$7375 = P (1 + 5% × 5)
⇒ $7375 = P (1 + 5/100 × 5)
⇒ $7375 = P (1 + 5 × 5/100)
⇒ $7375 = P (1 + 25/100)
⇒ $7375 = P (100 + 25/100)
⇒ $7375 = P × 125/100
⇒ P × 125/100 = $7375
⇒ P = 7375/125/100
⇒ P = 7375 × 100/125
⇒ P = 7375 × 100/125
⇒ P = 737500/125
⇒ P = $5900
Thus, the sum borrowed (P) = $5900 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 7375, then the Principal = 100/125 × 7375
= 100 × 7375/125
= 737500/125
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) 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.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(5) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(10) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.