Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $9240
Rate of Simple Interest (R) = 4%
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
$9240 = P (1 + 4% × 5)
⇒ $9240 = P (1 + 4/100 × 5)
⇒ $9240 = P (1 + 4 × 5/100)
⇒ $9240 = P (1 + 20/100)
⇒ $9240 = P (100 + 20/100)
⇒ $9240 = P × 120/100
⇒ P × 120/100 = $9240
⇒ P = 9240/120/100
⇒ P = 9240 × 100/120
⇒ P = 9240 × 100/120
⇒ P = 924000/120
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9240, then the Principal = 100/120 × 9240
= 100 × 9240/120
= 924000/120
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(5) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(6) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(10) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?