Question:
Elizabeth had to pay $3760.5 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
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3760.5
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
$3760.5 = P (1 + 3% × 3)
⇒ $3760.5 = P (1 + 3/100 × 3)
⇒ $3760.5 = P (1 + 3 × 3/100)
⇒ $3760.5 = P (1 + 9/100)
⇒ $3760.5 = P (100 + 9/100)
⇒ $3760.5 = P × 109/100
⇒ P × 109/100 = $3760.5
⇒ P = 3760.5/109/100
⇒ P = 3760.5 × 100/109
⇒ P = 3760.5 × 100/109
⇒ P = 376050/109
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 3760.5, then the Principal = 100/109 × 3760.5
= 100 × 3760.5/109
= 376050/109
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(2) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(7) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.