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) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(3) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.