Question:
If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4500
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
$4500 = P (1 + 5% × 4)
⇒ $4500 = P (1 + 5/100 × 4)
⇒ $4500 = P (1 + 5 × 4/100)
⇒ $4500 = P (1 + 20/100)
⇒ $4500 = P (100 + 20/100)
⇒ $4500 = P × 120/100
⇒ P × 120/100 = $4500
⇒ P = 4500/120/100
⇒ P = 4500 × 100/120
⇒ P = 4500 × 100/120
⇒ P = 450000/120
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 4500, then the Principal = 100/120 × 4500
= 100 × 4500/120
= 450000/120
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(3) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?
(7) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?