Question:
If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5400
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
$5400 = P (1 + 2% × 4)
⇒ $5400 = P (1 + 2/100 × 4)
⇒ $5400 = P (1 + 2 × 4/100)
⇒ $5400 = P (1 + 8/100)
⇒ $5400 = P (100 + 8/100)
⇒ $5400 = P × 108/100
⇒ P × 108/100 = $5400
⇒ P = 5400/108/100
⇒ P = 5400 × 100/108
⇒ P = 5400 × 100/108
⇒ P = 540000/108
⇒ 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 = 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 5400, then the Principal = 100/108 × 5400
= 100 × 5400/108
= 540000/108
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.