Question:
If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4536
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
$4536 = P (1 + 3% × 4)
⇒ $4536 = P (1 + 3/100 × 4)
⇒ $4536 = P (1 + 3 × 4/100)
⇒ $4536 = P (1 + 12/100)
⇒ $4536 = P (100 + 12/100)
⇒ $4536 = P × 112/100
⇒ P × 112/100 = $4536
⇒ P = 4536/112/100
⇒ P = 4536 × 100/112
⇒ P = 4536 × 100/112
⇒ P = 453600/112
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4536, then the Principal = 100/112 × 4536
= 100 × 4536/112
= 453600/112
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(4) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(7) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.