Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $8460
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
$8460 = P (1 + 4% × 5)
⇒ $8460 = P (1 + 4/100 × 5)
⇒ $8460 = P (1 + 4 × 5/100)
⇒ $8460 = P (1 + 20/100)
⇒ $8460 = P (100 + 20/100)
⇒ $8460 = P × 120/100
⇒ P × 120/100 = $8460
⇒ P = 8460/120/100
⇒ P = 8460 × 100/120
⇒ P = 8460 × 100/120
⇒ P = 846000/120
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 8460, then the Principal = 100/120 × 8460
= 100 × 8460/120
= 846000/120
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(2) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?