Question:
William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $4025
Rate of Simple Interest (R) = 5%
Time (T) = 3 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
$4025 = P (1 + 5% × 3)
⇒ $4025 = P (1 + 5/100 × 3)
⇒ $4025 = P (1 + 5 × 3/100)
⇒ $4025 = P (1 + 15/100)
⇒ $4025 = P (100 + 15/100)
⇒ $4025 = P × 115/100
⇒ P × 115/100 = $4025
⇒ P = 4025/115/100
⇒ P = 4025 × 100/115
⇒ P = 4025 × 100/115
⇒ P = 402500/115
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 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 4025, then the Principal = 100/115 × 4025
= 100 × 4025/115
= 402500/115
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(5) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(7) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.