Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $7920
Rate of Simple Interest (R) = 2%
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
$7920 = P (1 + 2% × 5)
⇒ $7920 = P (1 + 2/100 × 5)
⇒ $7920 = P (1 + 2 × 5/100)
⇒ $7920 = P (1 + 10/100)
⇒ $7920 = P (100 + 10/100)
⇒ $7920 = P × 110/100
⇒ P × 110/100 = $7920
⇒ P = 7920/110/100
⇒ P = 7920 × 100/110
⇒ P = 7920 × 100/110
⇒ P = 792000/110
⇒ P = $7200
Thus, the sum borrowed (P) = $7200 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 = 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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7920, then the Principal = 100/110 × 7920
= 100 × 7920/110
= 792000/110
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?