Question:
Christopher had to pay $4600 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
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4600
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
$4600 = P (1 + 5% × 3)
⇒ $4600 = P (1 + 5/100 × 3)
⇒ $4600 = P (1 + 5 × 3/100)
⇒ $4600 = P (1 + 15/100)
⇒ $4600 = P (100 + 15/100)
⇒ $4600 = P × 115/100
⇒ P × 115/100 = $4600
⇒ P = 4600/115/100
⇒ P = 4600 × 100/115
⇒ P = 4600 × 100/115
⇒ P = 460000/115
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4600, then the Principal = 100/115 × 4600
= 100 × 4600/115
= 460000/115
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(3) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(5) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.