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) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(7) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.