Question:
Nancy had to pay $4523.5 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4523.5
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
$4523.5 = P (1 + 3% × 3)
⇒ $4523.5 = P (1 + 3/100 × 3)
⇒ $4523.5 = P (1 + 3 × 3/100)
⇒ $4523.5 = P (1 + 9/100)
⇒ $4523.5 = P (100 + 9/100)
⇒ $4523.5 = P × 109/100
⇒ P × 109/100 = $4523.5
⇒ P = 4523.5/109/100
⇒ P = 4523.5 × 100/109
⇒ P = 4523.5 × 100/109
⇒ P = 452350/109
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 4523.5, then the Principal = 100/109 × 4523.5
= 100 × 4523.5/109
= 452350/109
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(3) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(7) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.