Question:
Richard had to pay $4140 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
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $4140
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
$4140 = P (1 + 5% × 3)
⇒ $4140 = P (1 + 5/100 × 3)
⇒ $4140 = P (1 + 5 × 3/100)
⇒ $4140 = P (1 + 15/100)
⇒ $4140 = P (100 + 15/100)
⇒ $4140 = P × 115/100
⇒ P × 115/100 = $4140
⇒ P = 4140/115/100
⇒ P = 4140 × 100/115
⇒ P = 4140 × 100/115
⇒ P = 414000/115
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 4140, then the Principal = 100/115 × 4140
= 100 × 4140/115
= 414000/115
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(4) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(7) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.