Question:
How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $7080
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$7080 = P (1 + 4% × 5)
⇒ $7080 = P (1 + 4/100 × 5)
⇒ $7080 = P (1 + 4 × 5/100)
⇒ $7080 = P (1 + 20/100)
⇒ $7080 = P (100 + 20/100)
⇒ $7080 = P × 120/100
⇒ P × 120/100 = $7080
⇒ P = 7080/120/100
⇒ P = 7080 × 100/120
⇒ P = 7080 × 100/120
⇒ P = 708000/120
⇒ P = $5900
Thus, the sum borrowed (P) = $5900 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 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 7080, then the Principal = 100/120 × 7080
= 100 × 7080/120
= 708000/120
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(4) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(7) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(9) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?