Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7320
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
$7320 = P (1 + 4% × 5)
⇒ $7320 = P (1 + 4/100 × 5)
⇒ $7320 = P (1 + 4 × 5/100)
⇒ $7320 = P (1 + 20/100)
⇒ $7320 = P (100 + 20/100)
⇒ $7320 = P × 120/100
⇒ P × 120/100 = $7320
⇒ P = 7320/120/100
⇒ P = 7320 × 100/120
⇒ P = 7320 × 100/120
⇒ P = 732000/120
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 7320, then the Principal = 100/120 × 7320
= 100 × 7320/120
= 732000/120
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(4) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(9) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.