Question:
If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $4140
Rate of Simple Interest (R) = 5%
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
$4140 = P (1 + 5% × 4)
⇒ $4140 = P (1 + 5/100 × 4)
⇒ $4140 = P (1 + 5 × 4/100)
⇒ $4140 = P (1 + 20/100)
⇒ $4140 = P (100 + 20/100)
⇒ $4140 = P × 120/100
⇒ P × 120/100 = $4140
⇒ P = 4140/120/100
⇒ P = 4140 × 100/120
⇒ P = 4140 × 100/120
⇒ P = 414000/120
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4140, then the Principal = 100/120 × 4140
= 100 × 4140/120
= 414000/120
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(2) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.