Question:
How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $6210
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$6210 = P (1 + 3% × 5)
⇒ $6210 = P (1 + 3/100 × 5)
⇒ $6210 = P (1 + 3 × 5/100)
⇒ $6210 = P (1 + 15/100)
⇒ $6210 = P (100 + 15/100)
⇒ $6210 = P × 115/100
⇒ P × 115/100 = $6210
⇒ P = 6210/115/100
⇒ P = 6210 × 100/115
⇒ P = 6210 × 100/115
⇒ P = 621000/115
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6210, then the Principal = 100/115 × 6210
= 100 × 6210/115
= 621000/115
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(10) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.