Question:
Michelle had to pay $5692.5 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
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5692.5
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
$5692.5 = P (1 + 5% × 3)
⇒ $5692.5 = P (1 + 5/100 × 3)
⇒ $5692.5 = P (1 + 5 × 3/100)
⇒ $5692.5 = P (1 + 15/100)
⇒ $5692.5 = P (100 + 15/100)
⇒ $5692.5 = P × 115/100
⇒ P × 115/100 = $5692.5
⇒ P = 5692.5/115/100
⇒ P = 5692.5 × 100/115
⇒ P = 5692.5 × 100/115
⇒ P = 569250/115
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5692.5, then the Principal = 100/115 × 5692.5
= 100 × 5692.5/115
= 569250/115
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(7) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(9) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.