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 Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(2) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(4) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.