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) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(8) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.