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) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(5) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) 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.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(10) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.