Question:
Joseph had to pay $4255 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
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4255
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
$4255 = P (1 + 5% × 3)
⇒ $4255 = P (1 + 5/100 × 3)
⇒ $4255 = P (1 + 5 × 3/100)
⇒ $4255 = P (1 + 15/100)
⇒ $4255 = P (100 + 15/100)
⇒ $4255 = P × 115/100
⇒ P × 115/100 = $4255
⇒ P = 4255/115/100
⇒ P = 4255 × 100/115
⇒ P = 4255 × 100/115
⇒ P = 425500/115
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 4255, then the Principal = 100/115 × 4255
= 100 × 4255/115
= 425500/115
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(3) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(6) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(10) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.