Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 5% × 5)
⇒ $8625 = P (1 + 5/100 × 5)
⇒ $8625 = P (1 + 5 × 5/100)
⇒ $8625 = P (1 + 25/100)
⇒ $8625 = P (100 + 25/100)
⇒ $8625 = P × 125/100
⇒ P × 125/100 = $8625
⇒ P = 8625/125/100
⇒ P = 8625 × 100/125
⇒ P = 8625 × 100/125
⇒ P = 862500/125
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8625, then the Principal = 100/125 × 8625
= 100 × 8625/125
= 862500/125
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(3) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.