Question:
How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6325
Rate of Simple Interest (R) = 3%
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
$6325 = P (1 + 3% × 5)
⇒ $6325 = P (1 + 3/100 × 5)
⇒ $6325 = P (1 + 3 × 5/100)
⇒ $6325 = P (1 + 15/100)
⇒ $6325 = P (100 + 15/100)
⇒ $6325 = P × 115/100
⇒ P × 115/100 = $6325
⇒ P = 6325/115/100
⇒ P = 6325 × 100/115
⇒ P = 6325 × 100/115
⇒ P = 632500/115
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6325, then the Principal = 100/115 × 6325
= 100 × 6325/115
= 632500/115
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(7) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(10) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.