Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8937.5
Rate of Simple Interest (R) = 5%
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
$8937.5 = P (1 + 5% × 5)
⇒ $8937.5 = P (1 + 5/100 × 5)
⇒ $8937.5 = P (1 + 5 × 5/100)
⇒ $8937.5 = P (1 + 25/100)
⇒ $8937.5 = P (100 + 25/100)
⇒ $8937.5 = P × 125/100
⇒ P × 125/100 = $8937.5
⇒ P = 8937.5/125/100
⇒ P = 8937.5 × 100/125
⇒ P = 8937.5 × 100/125
⇒ P = 893750/125
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8937.5, then the Principal = 100/125 × 8937.5
= 100 × 8937.5/125
= 893750/125
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(6) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(8) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(10) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.