Question:
Charles had to pay $4251 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
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4251
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
$4251 = P (1 + 3% × 3)
⇒ $4251 = P (1 + 3/100 × 3)
⇒ $4251 = P (1 + 3 × 3/100)
⇒ $4251 = P (1 + 9/100)
⇒ $4251 = P (100 + 9/100)
⇒ $4251 = P × 109/100
⇒ P × 109/100 = $4251
⇒ P = 4251/109/100
⇒ P = 4251 × 100/109
⇒ P = 4251 × 100/109
⇒ P = 425100/109
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4251, then the Principal = 100/109 × 4251
= 100 × 4251/109
= 425100/109
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(9) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?