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) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(2) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(4) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(8) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.