Question:
How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6325
Rate of Simple Interest (R) = 3%
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
$6325 = P (1 + 3% × 5)
⇒ $6325 = P (1 + 3/100 × 5)
⇒ $6325 = P (1 + 3 × 5/100)
⇒ $6325 = P (1 + 15/100)
⇒ $6325 = P (100 + 15/100)
⇒ $6325 = P × 115/100
⇒ P × 115/100 = $6325
⇒ P = 6325/115/100
⇒ P = 6325 × 100/115
⇒ P = 6325 × 100/115
⇒ P = 632500/115
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6325, then the Principal = 100/115 × 6325
= 100 × 6325/115
= 632500/115
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(2) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(8) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.