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) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(2) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(8) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?