Question:
Paul had to pay $4982 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
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $4982
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
$4982 = P (1 + 2% × 3)
⇒ $4982 = P (1 + 2/100 × 3)
⇒ $4982 = P (1 + 2 × 3/100)
⇒ $4982 = P (1 + 6/100)
⇒ $4982 = P (100 + 6/100)
⇒ $4982 = P × 106/100
⇒ P × 106/100 = $4982
⇒ P = 4982/106/100
⇒ P = 4982 × 100/106
⇒ P = 4982 × 100/106
⇒ P = 498200/106
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 4982, then the Principal = 100/106 × 4982
= 100 × 4982/106
= 498200/106
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
(3) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?