Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $9437.5
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
$9437.5 = P (1 + 5% × 5)
⇒ $9437.5 = P (1 + 5/100 × 5)
⇒ $9437.5 = P (1 + 5 × 5/100)
⇒ $9437.5 = P (1 + 25/100)
⇒ $9437.5 = P (100 + 25/100)
⇒ $9437.5 = P × 125/100
⇒ P × 125/100 = $9437.5
⇒ P = 9437.5/125/100
⇒ P = 9437.5 × 100/125
⇒ P = 9437.5 × 100/125
⇒ P = 943750/125
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 9437.5, then the Principal = 100/125 × 9437.5
= 100 × 9437.5/125
= 943750/125
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(2) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.