Question:
If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4640
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
$4640 = P (1 + 4% × 4)
⇒ $4640 = P (1 + 4/100 × 4)
⇒ $4640 = P (1 + 4 × 4/100)
⇒ $4640 = P (1 + 16/100)
⇒ $4640 = P (100 + 16/100)
⇒ $4640 = P × 116/100
⇒ P × 116/100 = $4640
⇒ P = 4640/116/100
⇒ P = 4640 × 100/116
⇒ P = 4640 × 100/116
⇒ P = 464000/116
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4640, then the Principal = 100/116 × 4640
= 100 × 4640/116
= 464000/116
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(10) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.