Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $9600
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
$9600 = P (1 + 4% × 5)
⇒ $9600 = P (1 + 4/100 × 5)
⇒ $9600 = P (1 + 4 × 5/100)
⇒ $9600 = P (1 + 20/100)
⇒ $9600 = P (100 + 20/100)
⇒ $9600 = P × 120/100
⇒ P × 120/100 = $9600
⇒ P = 9600/120/100
⇒ P = 9600 × 100/120
⇒ P = 9600 × 100/120
⇒ P = 960000/120
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 9600, then the Principal = 100/120 × 9600
= 100 × 9600/120
= 960000/120
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(3) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.