Question:
Mary had to pay $3507.5 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3507.5
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
$3507.5 = P (1 + 5% × 3)
⇒ $3507.5 = P (1 + 5/100 × 3)
⇒ $3507.5 = P (1 + 5 × 3/100)
⇒ $3507.5 = P (1 + 15/100)
⇒ $3507.5 = P (100 + 15/100)
⇒ $3507.5 = P × 115/100
⇒ P × 115/100 = $3507.5
⇒ P = 3507.5/115/100
⇒ P = 3507.5 × 100/115
⇒ P = 3507.5 × 100/115
⇒ P = 350750/115
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3507.5, then the Principal = 100/115 × 3507.5
= 100 × 3507.5/115
= 350750/115
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(4) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(10) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.