Question:
John had to pay $3680 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
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3680
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
$3680 = P (1 + 5% × 3)
⇒ $3680 = P (1 + 5/100 × 3)
⇒ $3680 = P (1 + 5 × 3/100)
⇒ $3680 = P (1 + 15/100)
⇒ $3680 = P (100 + 15/100)
⇒ $3680 = P × 115/100
⇒ P × 115/100 = $3680
⇒ P = 3680/115/100
⇒ P = 3680 × 100/115
⇒ P = 3680 × 100/115
⇒ P = 368000/115
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 3680, then the Principal = 100/115 × 3680
= 100 × 3680/115
= 368000/115
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(5) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(10) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.