Question:
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.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5177.5
Rate of Simple Interest (R) = 3%
Time (T) = 3 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
$5177.5 = P (1 + 3% × 3)
⇒ $5177.5 = P (1 + 3/100 × 3)
⇒ $5177.5 = P (1 + 3 × 3/100)
⇒ $5177.5 = P (1 + 9/100)
⇒ $5177.5 = P (100 + 9/100)
⇒ $5177.5 = P × 109/100
⇒ P × 109/100 = $5177.5
⇒ P = 5177.5/109/100
⇒ P = 5177.5 × 100/109
⇒ P = 5177.5 × 100/109
⇒ P = 517750/109
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5177.5, then the Principal = 100/109 × 5177.5
= 100 × 5177.5/109
= 517750/109
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?