Question:
If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5320
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
$5320 = P (1 + 3% × 4)
⇒ $5320 = P (1 + 3/100 × 4)
⇒ $5320 = P (1 + 3 × 4/100)
⇒ $5320 = P (1 + 12/100)
⇒ $5320 = P (100 + 12/100)
⇒ $5320 = P × 112/100
⇒ P × 112/100 = $5320
⇒ P = 5320/112/100
⇒ P = 5320 × 100/112
⇒ P = 5320 × 100/112
⇒ P = 532000/112
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5320, then the Principal = 100/112 × 5320
= 100 × 5320/112
= 532000/112
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(5) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(10) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.