Question:
Kimberly had to pay $5347.5 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
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5347.5
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
$5347.5 = P (1 + 5% × 3)
⇒ $5347.5 = P (1 + 5/100 × 3)
⇒ $5347.5 = P (1 + 5 × 3/100)
⇒ $5347.5 = P (1 + 15/100)
⇒ $5347.5 = P (100 + 15/100)
⇒ $5347.5 = P × 115/100
⇒ P × 115/100 = $5347.5
⇒ P = 5347.5/115/100
⇒ P = 5347.5 × 100/115
⇒ P = 5347.5 × 100/115
⇒ P = 534750/115
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5347.5, then the Principal = 100/115 × 5347.5
= 100 × 5347.5/115
= 534750/115
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(2) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(8) 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.
(9) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.