Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $9562.5
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
$9562.5 = P (1 + 5% × 5)
⇒ $9562.5 = P (1 + 5/100 × 5)
⇒ $9562.5 = P (1 + 5 × 5/100)
⇒ $9562.5 = P (1 + 25/100)
⇒ $9562.5 = P (100 + 25/100)
⇒ $9562.5 = P × 125/100
⇒ P × 125/100 = $9562.5
⇒ P = 9562.5/125/100
⇒ P = 9562.5 × 100/125
⇒ P = 9562.5 × 100/125
⇒ P = 956250/125
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 9562.5, then the Principal = 100/125 × 9562.5
= 100 × 9562.5/125
= 956250/125
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(2) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(9) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.