Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $9250
Rate of Simple Interest (R) = 5%
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
$9250 = P (1 + 5% × 5)
⇒ $9250 = P (1 + 5/100 × 5)
⇒ $9250 = P (1 + 5 × 5/100)
⇒ $9250 = P (1 + 25/100)
⇒ $9250 = P (100 + 25/100)
⇒ $9250 = P × 125/100
⇒ P × 125/100 = $9250
⇒ P = 9250/125/100
⇒ P = 9250 × 100/125
⇒ P = 9250 × 100/125
⇒ P = 925000/125
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9250, then the Principal = 100/125 × 9250
= 100 × 9250/125
= 925000/125
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(10) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?