Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $9360
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
$9360 = P (1 + 4% × 5)
⇒ $9360 = P (1 + 4/100 × 5)
⇒ $9360 = P (1 + 4 × 5/100)
⇒ $9360 = P (1 + 20/100)
⇒ $9360 = P (100 + 20/100)
⇒ $9360 = P × 120/100
⇒ P × 120/100 = $9360
⇒ P = 9360/120/100
⇒ P = 9360 × 100/120
⇒ P = 9360 × 100/120
⇒ P = 936000/120
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 9360, then the Principal = 100/120 × 9360
= 100 × 9360/120
= 936000/120
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.
(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(7) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.