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 Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(7) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.