Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $5775
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
$5775 = P (1 + 2% × 5)
⇒ $5775 = P (1 + 2/100 × 5)
⇒ $5775 = P (1 + 2 × 5/100)
⇒ $5775 = P (1 + 10/100)
⇒ $5775 = P (100 + 10/100)
⇒ $5775 = P × 110/100
⇒ P × 110/100 = $5775
⇒ P = 5775/110/100
⇒ P = 5775 × 100/110
⇒ P = 5775 × 100/110
⇒ P = 577500/110
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 5775, then the Principal = 100/110 × 5775
= 100 × 5775/110
= 577500/110
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(6) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.