Question:
If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5076
Rate of Simple Interest (R) = 2%
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
$5076 = P (1 + 2% × 4)
⇒ $5076 = P (1 + 2/100 × 4)
⇒ $5076 = P (1 + 2 × 4/100)
⇒ $5076 = P (1 + 8/100)
⇒ $5076 = P (100 + 8/100)
⇒ $5076 = P × 108/100
⇒ P × 108/100 = $5076
⇒ P = 5076/108/100
⇒ P = 5076 × 100/108
⇒ P = 5076 × 100/108
⇒ P = 507600/108
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5076, then the Principal = 100/108 × 5076
= 100 × 5076/108
= 507600/108
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(2) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(6) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(8) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.