Question:
Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4240
Rate of Simple Interest (R) = 2%
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
$4240 = P (1 + 2% × 3)
⇒ $4240 = P (1 + 2/100 × 3)
⇒ $4240 = P (1 + 2 × 3/100)
⇒ $4240 = P (1 + 6/100)
⇒ $4240 = P (100 + 6/100)
⇒ $4240 = P × 106/100
⇒ P × 106/100 = $4240
⇒ P = 4240/106/100
⇒ P = 4240 × 100/106
⇒ P = 4240 × 100/106
⇒ P = 424000/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4240, then the Principal = 100/106 × 4240
= 100 × 4240/106
= 424000/106
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(2) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(7) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?