Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6727.5
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
$6727.5 = P (1 + 3% × 5)
⇒ $6727.5 = P (1 + 3/100 × 5)
⇒ $6727.5 = P (1 + 3 × 5/100)
⇒ $6727.5 = P (1 + 15/100)
⇒ $6727.5 = P (100 + 15/100)
⇒ $6727.5 = P × 115/100
⇒ P × 115/100 = $6727.5
⇒ P = 6727.5/115/100
⇒ P = 6727.5 × 100/115
⇒ P = 6727.5 × 100/115
⇒ P = 672750/115
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 6727.5, then the Principal = 100/115 × 6727.5
= 100 × 6727.5/115
= 672750/115
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(7) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.