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) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(4) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.