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) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(3) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?