Question:
If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5400
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
$5400 = P (1 + 5% × 4)
⇒ $5400 = P (1 + 5/100 × 4)
⇒ $5400 = P (1 + 5 × 4/100)
⇒ $5400 = P (1 + 20/100)
⇒ $5400 = P (100 + 20/100)
⇒ $5400 = P × 120/100
⇒ P × 120/100 = $5400
⇒ P = 5400/120/100
⇒ P = 5400 × 100/120
⇒ P = 5400 × 100/120
⇒ P = 540000/120
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 5400, then the Principal = 100/120 × 5400
= 100 × 5400/120
= 540000/120
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(6) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?