Question:
Kenneth had to pay $5450 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
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5450
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
$5450 = P (1 + 3% × 3)
⇒ $5450 = P (1 + 3/100 × 3)
⇒ $5450 = P (1 + 3 × 3/100)
⇒ $5450 = P (1 + 9/100)
⇒ $5450 = P (100 + 9/100)
⇒ $5450 = P × 109/100
⇒ P × 109/100 = $5450
⇒ P = 5450/109/100
⇒ P = 5450 × 100/109
⇒ P = 5450 × 100/109
⇒ P = 545000/109
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 5450, then the Principal = 100/109 × 5450
= 100 × 5450/109
= 545000/109
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.