Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9027.5
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
$9027.5 = P (1 + 3% × 5)
⇒ $9027.5 = P (1 + 3/100 × 5)
⇒ $9027.5 = P (1 + 3 × 5/100)
⇒ $9027.5 = P (1 + 15/100)
⇒ $9027.5 = P (100 + 15/100)
⇒ $9027.5 = P × 115/100
⇒ P × 115/100 = $9027.5
⇒ P = 9027.5/115/100
⇒ P = 9027.5 × 100/115
⇒ P = 9027.5 × 100/115
⇒ P = 902750/115
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 9027.5, then the Principal = 100/115 × 9027.5
= 100 × 9027.5/115
= 902750/115
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(5) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.