Question:
Richard had to pay $3924 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
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $3924
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
$3924 = P (1 + 3% × 3)
⇒ $3924 = P (1 + 3/100 × 3)
⇒ $3924 = P (1 + 3 × 3/100)
⇒ $3924 = P (1 + 9/100)
⇒ $3924 = P (100 + 9/100)
⇒ $3924 = P × 109/100
⇒ P × 109/100 = $3924
⇒ P = 3924/109/100
⇒ P = 3924 × 100/109
⇒ P = 3924 × 100/109
⇒ P = 392400/109
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 3924, then the Principal = 100/109 × 3924
= 100 × 3924/109
= 392400/109
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(9) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.