Question:
If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4872
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$4872 = P (1 + 3% × 4)
⇒ $4872 = P (1 + 3/100 × 4)
⇒ $4872 = P (1 + 3 × 4/100)
⇒ $4872 = P (1 + 12/100)
⇒ $4872 = P (100 + 12/100)
⇒ $4872 = P × 112/100
⇒ P × 112/100 = $4872
⇒ P = 4872/112/100
⇒ P = 4872 × 100/112
⇒ P = 4872 × 100/112
⇒ P = 487200/112
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4872, then the Principal = 100/112 × 4872
= 100 × 4872/112
= 487200/112
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(5) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(7) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(9) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.