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) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?