Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8140
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
$8140 = P (1 + 2% × 5)
⇒ $8140 = P (1 + 2/100 × 5)
⇒ $8140 = P (1 + 2 × 5/100)
⇒ $8140 = P (1 + 10/100)
⇒ $8140 = P (100 + 10/100)
⇒ $8140 = P × 110/100
⇒ P × 110/100 = $8140
⇒ P = 8140/110/100
⇒ P = 8140 × 100/110
⇒ P = 8140 × 100/110
⇒ P = 814000/110
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8140, then the Principal = 100/110 × 8140
= 100 × 8140/110
= 814000/110
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.