Question:
How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5500
Rate of Simple Interest (R) = 2%
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
$5500 = P (1 + 2% × 5)
⇒ $5500 = P (1 + 2/100 × 5)
⇒ $5500 = P (1 + 2 × 5/100)
⇒ $5500 = P (1 + 10/100)
⇒ $5500 = P (100 + 10/100)
⇒ $5500 = P × 110/100
⇒ P × 110/100 = $5500
⇒ P = 5500/110/100
⇒ P = 5500 × 100/110
⇒ P = 5500 × 100/110
⇒ P = 550000/110
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5500, then the Principal = 100/110 × 5500
= 100 × 5500/110
= 550000/110
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(3) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(8) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(10) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.