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) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(4) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.