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) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(2) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(4) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(9) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(10) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.