Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $9312.5
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
$9312.5 = P (1 + 5% × 5)
⇒ $9312.5 = P (1 + 5/100 × 5)
⇒ $9312.5 = P (1 + 5 × 5/100)
⇒ $9312.5 = P (1 + 25/100)
⇒ $9312.5 = P (100 + 25/100)
⇒ $9312.5 = P × 125/100
⇒ P × 125/100 = $9312.5
⇒ P = 9312.5/125/100
⇒ P = 9312.5 × 100/125
⇒ P = 9312.5 × 100/125
⇒ P = 931250/125
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 9312.5, then the Principal = 100/125 × 9312.5
= 100 × 9312.5/125
= 931250/125
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(4) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(6) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(9) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(10) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?