Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $8062.5
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
$8062.5 = P (1 + 5% × 5)
⇒ $8062.5 = P (1 + 5/100 × 5)
⇒ $8062.5 = P (1 + 5 × 5/100)
⇒ $8062.5 = P (1 + 25/100)
⇒ $8062.5 = P (100 + 25/100)
⇒ $8062.5 = P × 125/100
⇒ P × 125/100 = $8062.5
⇒ P = 8062.5/125/100
⇒ P = 8062.5 × 100/125
⇒ P = 8062.5 × 100/125
⇒ P = 806250/125
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 8062.5, then the Principal = 100/125 × 8062.5
= 100 × 8062.5/125
= 806250/125
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.