Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $7130
Rate of Simple Interest (R) = 3%
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
$7130 = P (1 + 3% × 5)
⇒ $7130 = P (1 + 3/100 × 5)
⇒ $7130 = P (1 + 3 × 5/100)
⇒ $7130 = P (1 + 15/100)
⇒ $7130 = P (100 + 15/100)
⇒ $7130 = P × 115/100
⇒ P × 115/100 = $7130
⇒ P = 7130/115/100
⇒ P = 7130 × 100/115
⇒ P = 7130 × 100/115
⇒ P = 713000/115
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 7130, then the Principal = 100/115 × 7130
= 100 × 7130/115
= 713000/115
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?