Question:
Nancy had to pay $4772.5 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4772.5
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
$4772.5 = P (1 + 5% × 3)
⇒ $4772.5 = P (1 + 5/100 × 3)
⇒ $4772.5 = P (1 + 5 × 3/100)
⇒ $4772.5 = P (1 + 15/100)
⇒ $4772.5 = P (100 + 15/100)
⇒ $4772.5 = P × 115/100
⇒ P × 115/100 = $4772.5
⇒ P = 4772.5/115/100
⇒ P = 4772.5 × 100/115
⇒ P = 4772.5 × 100/115
⇒ P = 477250/115
⇒ 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 = 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 4772.5, then the Principal = 100/115 × 4772.5
= 100 × 4772.5/115
= 477250/115
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(2) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(9) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.