Question:
How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Amount (A) = $7590
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
$7590 = P (1 + 3% × 5)
⇒ $7590 = P (1 + 3/100 × 5)
⇒ $7590 = P (1 + 3 × 5/100)
⇒ $7590 = P (1 + 15/100)
⇒ $7590 = P (100 + 15/100)
⇒ $7590 = P × 115/100
⇒ P × 115/100 = $7590
⇒ P = 7590/115/100
⇒ P = 7590 × 100/115
⇒ P = 7590 × 100/115
⇒ P = 759000/115
⇒ P = $6600
Thus, the sum borrowed (P) = $6600 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 7590, then the Principal = 100/115 × 7590
= 100 × 7590/115
= 759000/115
= 6600
Thus, Principal = $6600
Thus, the sum borrowed = $6600 Answer
Similar Questions
(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.