Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $8250
Rate of Simple Interest (R) = 2%
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
$8250 = P (1 + 2% × 5)
⇒ $8250 = P (1 + 2/100 × 5)
⇒ $8250 = P (1 + 2 × 5/100)
⇒ $8250 = P (1 + 10/100)
⇒ $8250 = P (100 + 10/100)
⇒ $8250 = P × 110/100
⇒ P × 110/100 = $8250
⇒ P = 8250/110/100
⇒ P = 8250 × 100/110
⇒ P = 8250 × 100/110
⇒ P = 825000/110
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8250, then the Principal = 100/110 × 8250
= 100 × 8250/110
= 825000/110
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(3) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.