Question:
How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6875
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
$6875 = P (1 + 5% × 5)
⇒ $6875 = P (1 + 5/100 × 5)
⇒ $6875 = P (1 + 5 × 5/100)
⇒ $6875 = P (1 + 25/100)
⇒ $6875 = P (100 + 25/100)
⇒ $6875 = P × 125/100
⇒ P × 125/100 = $6875
⇒ P = 6875/125/100
⇒ P = 6875 × 100/125
⇒ P = 6875 × 100/125
⇒ P = 687500/125
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 6875, then the Principal = 100/125 × 6875
= 100 × 6875/125
= 687500/125
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.