Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6435
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
$6435 = P (1 + 2% × 5)
⇒ $6435 = P (1 + 2/100 × 5)
⇒ $6435 = P (1 + 2 × 5/100)
⇒ $6435 = P (1 + 10/100)
⇒ $6435 = P (100 + 10/100)
⇒ $6435 = P × 110/100
⇒ P × 110/100 = $6435
⇒ P = 6435/110/100
⇒ P = 6435 × 100/110
⇒ P = 6435 × 100/110
⇒ P = 643500/110
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 6435, then the Principal = 100/110 × 6435
= 100 × 6435/110
= 643500/110
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(5) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.