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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(8) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.