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 & 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) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(5) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.