Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7302.5
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
$7302.5 = P (1 + 3% × 5)
⇒ $7302.5 = P (1 + 3/100 × 5)
⇒ $7302.5 = P (1 + 3 × 5/100)
⇒ $7302.5 = P (1 + 15/100)
⇒ $7302.5 = P (100 + 15/100)
⇒ $7302.5 = P × 115/100
⇒ P × 115/100 = $7302.5
⇒ P = 7302.5/115/100
⇒ P = 7302.5 × 100/115
⇒ P = 7302.5 × 100/115
⇒ P = 730250/115
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7302.5, then the Principal = 100/115 × 7302.5
= 100 × 7302.5/115
= 730250/115
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.