Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6960
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
$6960 = P (1 + 4% × 5)
⇒ $6960 = P (1 + 4/100 × 5)
⇒ $6960 = P (1 + 4 × 5/100)
⇒ $6960 = P (1 + 20/100)
⇒ $6960 = P (100 + 20/100)
⇒ $6960 = P × 120/100
⇒ P × 120/100 = $6960
⇒ P = 6960/120/100
⇒ P = 6960 × 100/120
⇒ P = 6960 × 100/120
⇒ P = 696000/120
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 6960, then the Principal = 100/120 × 6960
= 100 × 6960/120
= 696000/120
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 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) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(4) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(10) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.