Question:
If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $4140
Rate of Simple Interest (R) = 5%
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
$4140 = P (1 + 5% × 4)
⇒ $4140 = P (1 + 5/100 × 4)
⇒ $4140 = P (1 + 5 × 4/100)
⇒ $4140 = P (1 + 20/100)
⇒ $4140 = P (100 + 20/100)
⇒ $4140 = P × 120/100
⇒ P × 120/100 = $4140
⇒ P = 4140/120/100
⇒ P = 4140 × 100/120
⇒ P = 4140 × 100/120
⇒ P = 414000/120
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 = 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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4140, then the Principal = 100/120 × 4140
= 100 × 4140/120
= 414000/120
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(3) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?
(7) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(8) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?