Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $5995
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
$5995 = P (1 + 2% × 5)
⇒ $5995 = P (1 + 2/100 × 5)
⇒ $5995 = P (1 + 2 × 5/100)
⇒ $5995 = P (1 + 10/100)
⇒ $5995 = P (100 + 10/100)
⇒ $5995 = P × 110/100
⇒ P × 110/100 = $5995
⇒ P = 5995/110/100
⇒ P = 5995 × 100/110
⇒ P = 5995 × 100/110
⇒ P = 599500/110
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 5995, then the Principal = 100/110 × 5995
= 100 × 5995/110
= 599500/110
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(9) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.