Question:
Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3433.5
Rate of Simple Interest (R) = 3%
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
$3433.5 = P (1 + 3% × 3)
⇒ $3433.5 = P (1 + 3/100 × 3)
⇒ $3433.5 = P (1 + 3 × 3/100)
⇒ $3433.5 = P (1 + 9/100)
⇒ $3433.5 = P (100 + 9/100)
⇒ $3433.5 = P × 109/100
⇒ P × 109/100 = $3433.5
⇒ P = 3433.5/109/100
⇒ P = 3433.5 × 100/109
⇒ P = 3433.5 × 100/109
⇒ P = 343350/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 3433.5, then the Principal = 100/109 × 3433.5
= 100 × 3433.5/109
= 343350/109
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(4) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(6) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(9) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.