Question:
Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4657.5
Rate of Simple Interest (R) = 5%
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
$4657.5 = P (1 + 5% × 3)
⇒ $4657.5 = P (1 + 5/100 × 3)
⇒ $4657.5 = P (1 + 5 × 3/100)
⇒ $4657.5 = P (1 + 15/100)
⇒ $4657.5 = P (100 + 15/100)
⇒ $4657.5 = P × 115/100
⇒ P × 115/100 = $4657.5
⇒ P = 4657.5/115/100
⇒ P = 4657.5 × 100/115
⇒ P = 4657.5 × 100/115
⇒ P = 465750/115
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 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 4657.5, then the Principal = 100/115 × 4657.5
= 100 × 4657.5/115
= 465750/115
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(5) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?