Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7937.5
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
$7937.5 = P (1 + 5% × 5)
⇒ $7937.5 = P (1 + 5/100 × 5)
⇒ $7937.5 = P (1 + 5 × 5/100)
⇒ $7937.5 = P (1 + 25/100)
⇒ $7937.5 = P (100 + 25/100)
⇒ $7937.5 = P × 125/100
⇒ P × 125/100 = $7937.5
⇒ P = 7937.5/125/100
⇒ P = 7937.5 × 100/125
⇒ P = 7937.5 × 100/125
⇒ P = 793750/125
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7937.5, then the Principal = 100/125 × 7937.5
= 100 × 7937.5/125
= 793750/125
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(4) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(6) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.