Question:
If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $5046
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
$5046 = P (1 + 4% × 4)
⇒ $5046 = P (1 + 4/100 × 4)
⇒ $5046 = P (1 + 4 × 4/100)
⇒ $5046 = P (1 + 16/100)
⇒ $5046 = P (100 + 16/100)
⇒ $5046 = P × 116/100
⇒ P × 116/100 = $5046
⇒ P = 5046/116/100
⇒ P = 5046 × 100/116
⇒ P = 5046 × 100/116
⇒ P = 504600/116
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 5046, then the Principal = 100/116 × 5046
= 100 × 5046/116
= 504600/116
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(4) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(7) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.