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) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.