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) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(4) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(10) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.