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) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(6) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(7) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.