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) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(8) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.