Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9000
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
$9000 = P (1 + 4% × 5)
⇒ $9000 = P (1 + 4/100 × 5)
⇒ $9000 = P (1 + 4 × 5/100)
⇒ $9000 = P (1 + 20/100)
⇒ $9000 = P (100 + 20/100)
⇒ $9000 = P × 120/100
⇒ P × 120/100 = $9000
⇒ P = 9000/120/100
⇒ P = 9000 × 100/120
⇒ P = 9000 × 100/120
⇒ P = 900000/120
⇒ 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 = 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 9000, then the Principal = 100/120 × 9000
= 100 × 9000/120
= 900000/120
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Jennifer took a loan of $4500 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.
(2) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(6) 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.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.