Question:
William had to pay $3710 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
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3710
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
$3710 = P (1 + 2% × 3)
⇒ $3710 = P (1 + 2/100 × 3)
⇒ $3710 = P (1 + 2 × 3/100)
⇒ $3710 = P (1 + 6/100)
⇒ $3710 = P (100 + 6/100)
⇒ $3710 = P × 106/100
⇒ P × 106/100 = $3710
⇒ P = 3710/106/100
⇒ P = 3710 × 100/106
⇒ P = 3710 × 100/106
⇒ P = 371000/106
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 3710, then the Principal = 100/106 × 3710
= 100 × 3710/106
= 371000/106
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 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) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.