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) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(3) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(7) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.