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) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(5) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(8) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?