Question:
If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4440
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
$4440 = P (1 + 5% × 4)
⇒ $4440 = P (1 + 5/100 × 4)
⇒ $4440 = P (1 + 5 × 4/100)
⇒ $4440 = P (1 + 20/100)
⇒ $4440 = P (100 + 20/100)
⇒ $4440 = P × 120/100
⇒ P × 120/100 = $4440
⇒ P = 4440/120/100
⇒ P = 4440 × 100/120
⇒ P = 4440 × 100/120
⇒ P = 444000/120
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 4440, then the Principal = 100/120 × 4440
= 100 × 4440/120
= 444000/120
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(5) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(8) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.