Question:
Charles had to pay $4485 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
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4485
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
$4485 = P (1 + 5% × 3)
⇒ $4485 = P (1 + 5/100 × 3)
⇒ $4485 = P (1 + 5 × 3/100)
⇒ $4485 = P (1 + 15/100)
⇒ $4485 = P (100 + 15/100)
⇒ $4485 = P × 115/100
⇒ P × 115/100 = $4485
⇒ P = 4485/115/100
⇒ P = 4485 × 100/115
⇒ P = 4485 × 100/115
⇒ P = 448500/115
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4485, then the Principal = 100/115 × 4485
= 100 × 4485/115
= 448500/115
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(2) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.