Question:
How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Amount (A) = $7700
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
$7700 = P (1 + 2% × 5)
⇒ $7700 = P (1 + 2/100 × 5)
⇒ $7700 = P (1 + 2 × 5/100)
⇒ $7700 = P (1 + 10/100)
⇒ $7700 = P (100 + 10/100)
⇒ $7700 = P × 110/100
⇒ P × 110/100 = $7700
⇒ P = 7700/110/100
⇒ P = 7700 × 100/110
⇒ P = 7700 × 100/110
⇒ P = 770000/110
⇒ P = $7000
Thus, the sum borrowed (P) = $7000 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 7700, then the Principal = 100/110 × 7700
= 100 × 7700/110
= 770000/110
= 7000
Thus, Principal = $7000
Thus, the sum borrowed = $7000 Answer
Similar Questions
(1) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
(8) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(10) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.