Question:
If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $6000
Rate of Simple Interest (R) = 5%
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
$6000 = P (1 + 5% × 4)
⇒ $6000 = P (1 + 5/100 × 4)
⇒ $6000 = P (1 + 5 × 4/100)
⇒ $6000 = P (1 + 20/100)
⇒ $6000 = P (100 + 20/100)
⇒ $6000 = P × 120/100
⇒ P × 120/100 = $6000
⇒ P = 6000/120/100
⇒ P = 6000 × 100/120
⇒ P = 6000 × 100/120
⇒ P = 600000/120
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6000, then the Principal = 100/120 × 6000
= 100 × 6000/120
= 600000/120
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(10) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.