Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6720
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
$6720 = P (1 + 4% × 5)
⇒ $6720 = P (1 + 4/100 × 5)
⇒ $6720 = P (1 + 4 × 5/100)
⇒ $6720 = P (1 + 20/100)
⇒ $6720 = P (100 + 20/100)
⇒ $6720 = P × 120/100
⇒ P × 120/100 = $6720
⇒ P = 6720/120/100
⇒ P = 6720 × 100/120
⇒ P = 6720 × 100/120
⇒ P = 672000/120
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 6720, then the Principal = 100/120 × 6720
= 100 × 6720/120
= 672000/120
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(2) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.