Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6267.5
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
$6267.5 = P (1 + 3% × 5)
⇒ $6267.5 = P (1 + 3/100 × 5)
⇒ $6267.5 = P (1 + 3 × 5/100)
⇒ $6267.5 = P (1 + 15/100)
⇒ $6267.5 = P (100 + 15/100)
⇒ $6267.5 = P × 115/100
⇒ P × 115/100 = $6267.5
⇒ P = 6267.5/115/100
⇒ P = 6267.5 × 100/115
⇒ P = 6267.5 × 100/115
⇒ P = 626750/115
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 6267.5, then the Principal = 100/115 × 6267.5
= 100 × 6267.5/115
= 626750/115
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(8) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(10) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?