Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $9180
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
$9180 = P (1 + 4% × 5)
⇒ $9180 = P (1 + 4/100 × 5)
⇒ $9180 = P (1 + 4 × 5/100)
⇒ $9180 = P (1 + 20/100)
⇒ $9180 = P (100 + 20/100)
⇒ $9180 = P × 120/100
⇒ P × 120/100 = $9180
⇒ P = 9180/120/100
⇒ P = 9180 × 100/120
⇒ P = 9180 × 100/120
⇒ P = 918000/120
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 9180, then the Principal = 100/120 × 9180
= 100 × 9180/120
= 918000/120
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(9) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.