Question:
How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Amount (A) = $7260
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
$7260 = P (1 + 2% × 5)
⇒ $7260 = P (1 + 2/100 × 5)
⇒ $7260 = P (1 + 2 × 5/100)
⇒ $7260 = P (1 + 10/100)
⇒ $7260 = P (100 + 10/100)
⇒ $7260 = P × 110/100
⇒ P × 110/100 = $7260
⇒ P = 7260/110/100
⇒ P = 7260 × 100/110
⇒ P = 7260 × 100/110
⇒ P = 726000/110
⇒ P = $6600
Thus, the sum borrowed (P) = $6600 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 7260, then the Principal = 100/110 × 7260
= 100 × 7260/110
= 726000/110
= 6600
Thus, Principal = $6600
Thus, the sum borrowed = $6600 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(8) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(10) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.