Question:
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.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4104
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
$4104 = P (1 + 2% × 4)
⇒ $4104 = P (1 + 2/100 × 4)
⇒ $4104 = P (1 + 2 × 4/100)
⇒ $4104 = P (1 + 8/100)
⇒ $4104 = P (100 + 8/100)
⇒ $4104 = P × 108/100
⇒ P × 108/100 = $4104
⇒ P = 4104/108/100
⇒ P = 4104 × 100/108
⇒ P = 4104 × 100/108
⇒ P = 410400/108
⇒ 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 = 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 4104, then the Principal = 100/108 × 4104
= 100 × 4104/108
= 410400/108
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(4) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.