Question:
If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $5096
Rate of Simple Interest (R) = 3%
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
$5096 = P (1 + 3% × 4)
⇒ $5096 = P (1 + 3/100 × 4)
⇒ $5096 = P (1 + 3 × 4/100)
⇒ $5096 = P (1 + 12/100)
⇒ $5096 = P (100 + 12/100)
⇒ $5096 = P × 112/100
⇒ P × 112/100 = $5096
⇒ P = 5096/112/100
⇒ P = 5096 × 100/112
⇒ P = 5096 × 100/112
⇒ P = 509600/112
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5096, then the Principal = 100/112 × 5096
= 100 × 5096/112
= 509600/112
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.