Question:
Patricia had to pay $3339 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
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3339
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
$3339 = P (1 + 2% × 3)
⇒ $3339 = P (1 + 2/100 × 3)
⇒ $3339 = P (1 + 2 × 3/100)
⇒ $3339 = P (1 + 6/100)
⇒ $3339 = P (100 + 6/100)
⇒ $3339 = P × 106/100
⇒ P × 106/100 = $3339
⇒ P = 3339/106/100
⇒ P = 3339 × 100/106
⇒ P = 3339 × 100/106
⇒ P = 333900/106
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 3339, then the Principal = 100/106 × 3339
= 100 × 3339/106
= 333900/106
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(5) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.