Question:
Betty had to pay $4632.5 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
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4632.5
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
$4632.5 = P (1 + 3% × 3)
⇒ $4632.5 = P (1 + 3/100 × 3)
⇒ $4632.5 = P (1 + 3 × 3/100)
⇒ $4632.5 = P (1 + 9/100)
⇒ $4632.5 = P (100 + 9/100)
⇒ $4632.5 = P × 109/100
⇒ P × 109/100 = $4632.5
⇒ P = 4632.5/109/100
⇒ P = 4632.5 × 100/109
⇒ P = 4632.5 × 100/109
⇒ P = 463250/109
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 4632.5, then the Principal = 100/109 × 4632.5
= 100 × 4632.5/109
= 463250/109
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(5) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.