Question:
Karen had to pay $4542.5 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
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4542.5
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
$4542.5 = P (1 + 5% × 3)
⇒ $4542.5 = P (1 + 5/100 × 3)
⇒ $4542.5 = P (1 + 5 × 3/100)
⇒ $4542.5 = P (1 + 15/100)
⇒ $4542.5 = P (100 + 15/100)
⇒ $4542.5 = P × 115/100
⇒ P × 115/100 = $4542.5
⇒ P = 4542.5/115/100
⇒ P = 4542.5 × 100/115
⇒ P = 4542.5 × 100/115
⇒ P = 454250/115
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4542.5, then the Principal = 100/115 × 4542.5
= 100 × 4542.5/115
= 454250/115
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(2) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(9) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.