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) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
(4) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(5) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.