Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $7250
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
$7250 = P (1 + 5% × 5)
⇒ $7250 = P (1 + 5/100 × 5)
⇒ $7250 = P (1 + 5 × 5/100)
⇒ $7250 = P (1 + 25/100)
⇒ $7250 = P (100 + 25/100)
⇒ $7250 = P × 125/100
⇒ P × 125/100 = $7250
⇒ P = 7250/125/100
⇒ P = 7250 × 100/125
⇒ P = 7250 × 100/125
⇒ P = 725000/125
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 7250, then the Principal = 100/125 × 7250
= 100 × 7250/125
= 725000/125
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(9) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.