Question:
If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4536
Rate of Simple Interest (R) = 2%
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
$4536 = P (1 + 2% × 4)
⇒ $4536 = P (1 + 2/100 × 4)
⇒ $4536 = P (1 + 2 × 4/100)
⇒ $4536 = P (1 + 8/100)
⇒ $4536 = P (100 + 8/100)
⇒ $4536 = P × 108/100
⇒ P × 108/100 = $4536
⇒ P = 4536/108/100
⇒ P = 4536 × 100/108
⇒ P = 4536 × 100/108
⇒ P = 453600/108
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4536, then the Principal = 100/108 × 4536
= 100 × 4536/108
= 453600/108
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(8) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?