Question:
William had to pay $3815 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
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3815
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
$3815 = P (1 + 3% × 3)
⇒ $3815 = P (1 + 3/100 × 3)
⇒ $3815 = P (1 + 3 × 3/100)
⇒ $3815 = P (1 + 9/100)
⇒ $3815 = P (100 + 9/100)
⇒ $3815 = P × 109/100
⇒ P × 109/100 = $3815
⇒ P = 3815/109/100
⇒ P = 3815 × 100/109
⇒ P = 3815 × 100/109
⇒ P = 381500/109
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 3815, then the Principal = 100/109 × 3815
= 100 × 3815/109
= 381500/109
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(7) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.