Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $6375
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
$6375 = P (1 + 5% × 5)
⇒ $6375 = P (1 + 5/100 × 5)
⇒ $6375 = P (1 + 5 × 5/100)
⇒ $6375 = P (1 + 25/100)
⇒ $6375 = P (100 + 25/100)
⇒ $6375 = P × 125/100
⇒ P × 125/100 = $6375
⇒ P = 6375/125/100
⇒ P = 6375 × 100/125
⇒ P = 6375 × 100/125
⇒ P = 637500/125
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 6375, then the Principal = 100/125 × 6375
= 100 × 6375/125
= 637500/125
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(5) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.