Question:
If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4256
Rate of Simple Interest (R) = 3%
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
$4256 = P (1 + 3% × 4)
⇒ $4256 = P (1 + 3/100 × 4)
⇒ $4256 = P (1 + 3 × 4/100)
⇒ $4256 = P (1 + 12/100)
⇒ $4256 = P (100 + 12/100)
⇒ $4256 = P × 112/100
⇒ P × 112/100 = $4256
⇒ P = 4256/112/100
⇒ P = 4256 × 100/112
⇒ P = 4256 × 100/112
⇒ P = 425600/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4256, then the Principal = 100/112 × 4256
= 100 × 4256/112
= 425600/112
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(7) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.