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) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(9) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.