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) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(5) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.