Question:
Emily had to pay $5462.5 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
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5462.5
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
$5462.5 = P (1 + 5% × 3)
⇒ $5462.5 = P (1 + 5/100 × 3)
⇒ $5462.5 = P (1 + 5 × 3/100)
⇒ $5462.5 = P (1 + 15/100)
⇒ $5462.5 = P (100 + 15/100)
⇒ $5462.5 = P × 115/100
⇒ P × 115/100 = $5462.5
⇒ P = 5462.5/115/100
⇒ P = 5462.5 × 100/115
⇒ P = 5462.5 × 100/115
⇒ P = 546250/115
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5462.5, then the Principal = 100/115 × 5462.5
= 100 × 5462.5/115
= 546250/115
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(10) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.