Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7150
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
$7150 = P (1 + 2% × 5)
⇒ $7150 = P (1 + 2/100 × 5)
⇒ $7150 = P (1 + 2 × 5/100)
⇒ $7150 = P (1 + 10/100)
⇒ $7150 = P (100 + 10/100)
⇒ $7150 = P × 110/100
⇒ P × 110/100 = $7150
⇒ P = 7150/110/100
⇒ P = 7150 × 100/110
⇒ P = 7150 × 100/110
⇒ P = 715000/110
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7150, then the Principal = 100/110 × 7150
= 100 × 7150/110
= 715000/110
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(8) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?