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) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(4) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.
(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.