Question:
William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3920
Rate of Simple Interest (R) = 4%
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
$3920 = P (1 + 4% × 3)
⇒ $3920 = P (1 + 4/100 × 3)
⇒ $3920 = P (1 + 4 × 3/100)
⇒ $3920 = P (1 + 12/100)
⇒ $3920 = P (100 + 12/100)
⇒ $3920 = P × 112/100
⇒ P × 112/100 = $3920
⇒ P = 3920/112/100
⇒ P = 3920 × 100/112
⇒ P = 3920 × 100/112
⇒ P = 392000/112
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3920, then the Principal = 100/112 × 3920
= 100 × 3920/112
= 392000/112
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(2) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.
(4) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(7) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.