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) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(8) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.