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) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?