Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $6765
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
$6765 = P (1 + 2% × 5)
⇒ $6765 = P (1 + 2/100 × 5)
⇒ $6765 = P (1 + 2 × 5/100)
⇒ $6765 = P (1 + 10/100)
⇒ $6765 = P (100 + 10/100)
⇒ $6765 = P × 110/100
⇒ P × 110/100 = $6765
⇒ P = 6765/110/100
⇒ P = 6765 × 100/110
⇒ P = 6765 × 100/110
⇒ P = 676500/110
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 6765, then the Principal = 100/110 × 6765
= 100 × 6765/110
= 676500/110
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(6) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(7) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?