Question:
Lisa had to pay $4414.5 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
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4414.5
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
$4414.5 = P (1 + 3% × 3)
⇒ $4414.5 = P (1 + 3/100 × 3)
⇒ $4414.5 = P (1 + 3 × 3/100)
⇒ $4414.5 = P (1 + 9/100)
⇒ $4414.5 = P (100 + 9/100)
⇒ $4414.5 = P × 109/100
⇒ P × 109/100 = $4414.5
⇒ P = 4414.5/109/100
⇒ P = 4414.5 × 100/109
⇒ P = 4414.5 × 100/109
⇒ P = 441450/109
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4414.5, then the Principal = 100/109 × 4414.5
= 100 × 4414.5/109
= 441450/109
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(5) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.