Question:
If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4408
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
$4408 = P (1 + 4% × 4)
⇒ $4408 = P (1 + 4/100 × 4)
⇒ $4408 = P (1 + 4 × 4/100)
⇒ $4408 = P (1 + 16/100)
⇒ $4408 = P (100 + 16/100)
⇒ $4408 = P × 116/100
⇒ P × 116/100 = $4408
⇒ P = 4408/116/100
⇒ P = 4408 × 100/116
⇒ P = 4408 × 100/116
⇒ P = 440800/116
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4408, then the Principal = 100/116 × 4408
= 100 × 4408/116
= 440800/116
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(7) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.