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) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(2) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.