Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $9687.5
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
$9687.5 = P (1 + 5% × 5)
⇒ $9687.5 = P (1 + 5/100 × 5)
⇒ $9687.5 = P (1 + 5 × 5/100)
⇒ $9687.5 = P (1 + 25/100)
⇒ $9687.5 = P (100 + 25/100)
⇒ $9687.5 = P × 125/100
⇒ P × 125/100 = $9687.5
⇒ P = 9687.5/125/100
⇒ P = 9687.5 × 100/125
⇒ P = 9687.5 × 100/125
⇒ P = 968750/125
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 9687.5, then the Principal = 100/125 × 9687.5
= 100 × 9687.5/125
= 968750/125
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?