Question:
If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4872
Rate of Simple Interest (R) = 4%
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 + 4% × 4)
⇒ $4872 = P (1 + 4/100 × 4)
⇒ $4872 = P (1 + 4 × 4/100)
⇒ $4872 = P (1 + 16/100)
⇒ $4872 = P (100 + 16/100)
⇒ $4872 = P × 116/100
⇒ P × 116/100 = $4872
⇒ P = 4872/116/100
⇒ P = 4872 × 100/116
⇒ P = 4872 × 100/116
⇒ P = 487200/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4872, then the Principal = 100/116 × 4872
= 100 × 4872/116
= 487200/116
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.